###### Advertisements

###### Advertisements

Find the area of the rhombus, the length of whose diagonals are 30 cm and 16 cm. Also, find the perimeter of the rhombus.

###### Advertisements

#### Solution

Area of the rhombus =`1/2xxd_1xxd_2` Where `d_1 and d_2`

are the lengths of the diagonals

=`1/2xx30xx16`

=`240 cm^2`

Side of thee rhombus=`1/2 sqrt(d_1^2+d_2^2)`

=`1/2 sqrt(30^2+16^2)`

=`1/2sqrt1156`

=`1/2xx34`

= `17 cm`

Perimeter of the rhombus =4a

=`4xx17`

=`68 cm`

#### APPEARS IN

#### RELATED QUESTIONS

The radius of a circle is 7 cm. find the circumference of the circle.

An arc of a circle is of length 5π cm and the sector it bounds has an area of 20 π cm2. Find the radius of the circle.

Find the circumference of the circle with the following radius (Take `pi = 22/7`)

14 cm

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

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

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15. ( Take π = 3.14)

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 steel wire when bent is the form of square encloses an area of 12 cm2. If the same wire is bent in form of circle. Find the area of circle.

Below fig shows a sector of a circle, centre O. containing an angle 𝜃°. Prove that Perimeter of shaded region is 𝑟 (tan 𝜃 + sec 𝜃 +`(pitheta)/180`− 1)

^{°},

In the given figure, O is the centre of the sector. \[\angle\]ROQ = \[\angle\]MON = 60^{°} . OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. (\[\pi = \frac{22}{7}\])

^{° }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.

In the given figure,

\[\square\] PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y, and z.

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

Choose the correct alternative answer for the following question.

**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.**

^{3}.

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

The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers is 800 revolutions.

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.

The area of an equilateral triangle is `49sqrt(3)` cm^{2} . Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. [Take π = 1.73]

The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.

The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is

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

Height = 12 cm , radius = 5 cm

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

Radius= 10.5 cm

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

Diameter= 35 cm

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 of a circle is equal to the perimeter of a square. The area of the square is 484 sq. m. Find the area of the circle.

A conical tent with a capacity of 600 m^{3} stands on a circular base of area 160 m^{2} Find in m^{2} the area of the canvas.

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.

The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm^{2} Find the radii of the two circles.

A circus tent is cylindrical to a height of 5 m and conical above it. If its diameter is 42 m and slant height of the cone is 53 m, calculate the total area of the canvas required.

The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13. 2 cm. Find the radii of the two circles.

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 .

A horse is tied with a 21 m laig rope to the corner of a field which is in the shape of an equilateral triangle. Find the area of the field over which it can graze.

Find the circumference of the circle whose area is 81π cm ^{2}.

The speed of the car is 66 km/hour. If each wheel of the car is 140 cm in diameter, find the number of revolutions made by each wheel per minute.

A cart wheel makes 9 revolutions per second. If the diameter of the wheel is 42 cm, find its speed in km/hr.

Find the volume and the surface area of the spheres in the following :

Radius = 7 cm

Find the diameter of the sphere for the following :

Surface Area = 221. 76 cm^{2}

In the given figure, the area of the shaded portion is 770 cm^{2}. If the circumference of the outer circle is 132 cm, find the width of the shaded portion.

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°.

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

The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (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 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.

Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.

The circumference of a circle exceeds its diameter by 18 cm. find the radius of the circle.

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 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.

A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket. (Take π =22/7)

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) |

_______ | _________ | 72.6 cm |

If the circumference of a circle is 176 cm, find its radius.

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?

Find the area and perimeter of the following semicircles: Radius = 1.4cm

Find the circumference of a circle whose area is 81πcm^{2}.

The circumference of a circle exceeds its diameter by 450 cm. Find the area of the circle.

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 area between the circumference of two concentric circles is 2464cm^{2}. If the inner circle has a circumference of 132cm, calculate the radius of the outer circle.

Find the circumference of the circle whose area is 25times the area of the circle with radius 7cm.

The circumference of a circle is equal to the perimeter of a square. The area of the square is 484 sq.m. Find the area of the circle.

The cost of fencing a circular field at the rate of Rs.250 per metre is Rs.55000. The field is to be ploughing at the rate of Rs.15 per m^{2}. Find the cost of ploughing the field.

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 = 28 mm

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

49 cm

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

91 mm

A ground is in the form of a circle whose diameter is 350 m. An athlete makes 4 revolutions. Find the distance covered by the athlete

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?

Formula used to find the circumference of a circle is

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

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

The cost of fencing a circular race course at the rate of ₹ 8 per metre is ₹ 2112. Find the diameter of the race course

The cost of decorating the circumference of a circular lawn of a house at the rate of ₹ 55 per metre is ₹ 16940. What is the radius of the lawn?

Circumference of a circle of diameter 5 cm is ______.

Circumference of a circle disc is 88 cm. Its radius is ______.

Area of circular garden with diameter 8 m is ______.

The area of a square is 100 cm^{2}. The circumference (in cm) of the largest circle cut of it is ______.

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

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.