###### Advertisements

###### Advertisements

Find the area and perimeter of the following semicircles: Diameter = 7cm

###### Advertisements

#### Solution

The radius of a Circle with diameter d is r = `"d"/(2)`

The Area of a Semi-circle with radius r = `(pi"r"^2)/(2)`

The Perimeter of a Semi-circle with radius r

= πr + 2r

= r(π + 2)

= `"r"(22/7 + 2)`

= `(36)/(7) xx "r"`

The radius of a Circle with diameter 7 is r

= `(7)/(2)`

= 3.5cm

The Area of a Semi-circle with radius 3.5

= `(pi(3.5)^2)/(2)`

= 19.25cm^{2}

The Perimeter of a Semi-circle with radius r

= π x 3.5 + 2 x 3.5

= 3.5(π + 2)

= `3.5(22/7 + 2)`

= `(36)/(7) xx 3.5`

= 25cm.

#### APPEARS IN

#### RELATED QUESTIONS

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.

If the circumference of a circular sheet is 154 m, find its radius. Also find the area of

the sheet. (Take `pi = 22/7`)

Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take `pi = 22/7`)

A doorway is decorated as shown in the figure. There are four semi-circles. BC, the diameter of the larger semi-circle is of length 84 cm. Centres of the three equal semicircles lie on BC. ABC is an isosceles triangle with AB = AC. If BO = OC, find the area of the shaded region. (Take `pi = 22/7`)

An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of 𝜋, radius of the circle.

Find the angle subtended at the centre of circle of radius ‘a’ cm by an arc of length

`(api)/4` 𝑐𝑚

The base of a right – angled triangle measures 48 cm and its hypotenuse measures 50 cm. Find the area of the triangle.

The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is `640m^2` , find the depth of the canal.

Find the circumferences of a circle whose radius is 7 cm.

^{°},

In the given figure, if A(P-ABC) = 154 cm^{2 }radius of the circle is 14 cm, find

(1) `∠APC`

(2) l ( arc ABC) .

^{° }find the area of the sector in case.

The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is 210^{°}, find the area of the sector in case.

The radius of a sector of a circle is 7 cm. If the measure of the arc of the sector is - three right angles; find the area of the sector in case.

The area of a minor sector of a circle is 3.85 cm^{2 }and the measure of its central angle is 36^{°}. Find the radius of the circle.

^{°}and its length is 44 cm, find the circumference of the circle.

**Choose the correct alternative answer for the following question.**

The curved surface area of a cylinder is 440 cm 2 and its radius is 5 cm. Find its height.

Choose the correct alternative answer for the following question.

A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.

Choose the correct alternative answer for the following question.

**Choose the correct alternative answer for the following question.**

^{3}.

The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr ?

The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.

In the given figure, ABCD is a trapezium of area 24.5 cm^{2} , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region.

Radii of the circles are given below, find their areas.

(1) 28 cm

(2) 10.5 cm

(3) 17.5 cm

Areas of some circles are given below find their diameters.

(1) 176 sq cm

(2) 394.24 sq cm

(3) 12474 sq cm

Diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.

Find the area of the circle if its circumfence is 88 cm.

Find the area and perimeter of the circle with the following :

Radius= 2.8 cm

Find the area and perimeter of the circle with the following :

Radius= 10.5 cm

Find the curved surface area , the total surface area and the volume of a cone if its :

Height = 16 cm , diameter = 24 cm

The area of a circular ring enclosed between two concentric circles is 88 cm 2. Find the radii of the two circles, if their difference is 1 cm.

Find the area enclosed between two concentric circles, if their radii are 6 cm and 13 cm respectively.

A wire when bent in the form of a square encloses an area of 484 cm^{2}. If the same wire is bent into the form of a circle, find the area of the circle.

A wire is in the form of a circle of radius 42 cm. It is bent into a square.

Determine the side of the square and compare the area of the regions enclosed in two cases.

A 7 m road surrounds a circular garden whose area is 5544 m^{2}. Find the area of the road and the cost of tarring it at the rate of Rs.150 per sq m.

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.

Find the area enclosed between two concentric cirdes of radii 6.3 cm and 8.4 cm. A third concentric circle is drawn outside the 8.4 cm circle, so that the area enclosed between it and 8.4 cm cirde is the same as that between two inner circles. Find the radii of the third circle correct to two decimal places .

Find the area and perimeter of the following sector :

Diameter = 42 cm, angle at the centre is 100·.

The wheel of the car makes 10 revolutions per second. If its diameter is 70 cm, find the speed of the car in km per hour.

A cylindrical beaker of 7 cm diameter is partly filled with water. Determine the number of spherical marbles of diameter 1.4 cm that are to be submerged in it to raise the water level by 5.6 cm

Find the diameter of the sphere for the following :

Volume = `523 17/21` cm^{3}

An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is 42 cm and each wheel makes 1200 revolutions per minute, find the speed of the train.

Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

Draw the circumcircle of Δ PMT in which PM = 5.4, P = 60°, M = 70°.

In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.

The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = `22/7`)

The radius of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π =`22/7`)

The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:**(i) **perimeter of the square.**(ii)** circumference of the circle.**(iii)** radius of the circle.

Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radius 15 cm and 8 cm.

Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radius 10 cm, 12 cm, and 18 cm.

The circumference of a circle is eigth time the circumference of the circle with a radius of 12 cm. Find its diameter.

The radius of two circles are in the ratio 3 : 5, find the ratio between their circumferences.

The circumferences of two circles are in the ratio 5: 7, find the ratio between their radius.

AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm^{2} calculate:

(i) The length of AC and

(ii) The circumference of circle

Construct an angle PQR = 45°. Mark a point S on QR such that QS = 4.5 cm. Construct a circle to touch PQ at Q and also to pass through S.

Construct the circumcircle of the ABC when BC = 6 cm, B = 55° and C = 70°.

A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.

The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:**(i)** the radius of the inner track.**(ii)** the radius of the outer circumference.**(iii)** the length of the outer circumference.**(iv) **the cost of fencing the outer circumference at the rate of ₹50 per m.

In the adjoining figure, the radius is 3.5 cm. Find:

(i) The area of the quarter of the circle correct to one decimal place.

(ii) The perimeter of the quarter of the circle correct to one decimal place. ( Take π = `22/7`)

In the adjoining figure, the crescent is formed by two circles which touch at the point A. O is the centre of bigger circle. If CB = 9 cm and DE = 5 cm, find the area of the shaded portion.

Complete the table below.

Radius (r) | Diameter (d) | Circumference (c) |

7 cm | ______ |
_______ |

Complete the table below.

Radius (r) | Diameter (d) | Circumference (c) |

_______ | 28 cm | _________ |

Complete the table below.

Radius (r) | Diameter (d) | Circumference (c) |

_______ | _________ | 616 cm |

Complete the table below.

Radius (r) | Diameter (d) | Circumference (c) |

_______ | _________ | 72.6 cm |

The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?

The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km?

The diameter of a circle is 5.6 cm. Find its circumference.

The diameter of the wheel of a cart is 1.05 m. How much distance will the cart cover in 1000 rotations of the wheel?

The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.

The sum of the circumference and diameter of a circle is 176 cm. Find the area of the circle.

Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.

A bucket is raised from a well by means of a rope wound round a wheel of diameter 35 cm. If the bucket ascends in 2 minutes with a uniform speed of 1.1 m per sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

The circumference o a garden roller is 280cm. How many revolutions does it make in moving 490m?

The diameter of a cycle wheel is `4(5)/(11)"cm"`. How many revolutions will it make in moving 6.3km?

A wire when bent in the form of a square encloses an area of 484cm^{2}. If the same wire is bent into the form of a circle, find the area of the circle.

A 4.2m wide road surrounds a circular plot whose circumference is 176m. Find the cost of paving the road at Rs.75per m^{2}.

The radius of a circular plot is 7.7 metres. How much will it cost to fence the plot with 3 rounds of wire at the rate of 50 rupees per metre?

The radius of the wheel of a bus is 0.7 m. How many rotations will a wheel complete while traveling a distance of 22 km?

Diameters of different circles are given below. Find their circumference (Take π = `22/7`)

d = 56 m

Diameters of different circles are given below. Find their circumference (Take π = `22/7`)

d = 28 mm

Find the circumference of the circles whose radii are given below.

91 mm

The diameter of a circular well is 4.2 m. What is its circumference?

The diameter of the bullock cart wheel is 1.4 m. Find the distance covered by it in 150 rotations?

A Rose garden is in the form of circle of radius 63 m. The gardener wants to fence it at the rate of ₹ 150 per metre. Find the cost of fencing?

In the formula, C = 2πr, ‘r’ refers to

If the circumference of a circle is 82π, then the value of ‘r’ is

Circumference of a circle is always ______.

A wheel of a car covers a distance of 3520 cm in 20 rotations. Find the radius of the wheel?

The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Find the number of revolutions made by a circular wheel of area 1.54 m^{2} in rolling a distance of 176 m.

In reference to a circle the value of π is equal to ______.

Area of circular garden with diameter 8 m is ______.

The distance around a circle is its ______.

Circumference ‘C’ of a circle can be found by multiplying diameter ‘d’ with ______.

Ishika has designed a small oval race track for her remote control car. Her design is shown in the given figure. What is the total distance around the track? Round your answer to the nearest whole centimetre.

A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the given figure. Find the area of shaded portion.

A photograph of Billiard/Snooker table has dimensions as `1/10`th of its actual size as shown in the given figure:

The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of ₹ 200 per m^{2}. Find the cost of polishing.