#### Chapters

#### Balbharati SSC Class 10 Mathematics 2

## Chapter 7 : Mensuration

#### Pages 145 - 146

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

Find the volume of a sphere of diameter 6 cm.

Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.

Find the surface area of a sphere of radius 7 cm.

The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm^{2} .The cone is placed

upon the cylinder. Volume of the solid figure so formed is 500 cm^{3 }. Find the total height of the figure.

In the given figure, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.

In the given figure, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper?

In the given figure shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and surface area of the toy from the measures shown in the figure (\[\pi = 3 . 14\])

Find the surface area and the volume of a beach ball shown in the figure

As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water .

#### Page 148

^{3 })

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its i) curved surface area

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its

ii) total surface area

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its

iii ) volume \[\pi\] = 3.14)

The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\])

circumference_{1} = 2

_{1}= 132

r

_{1 }= \[\frac{132}{\pi} = 134\]

_{2}=2

_{2}= 88

r

_{2}= \[\frac{88}{2\pi} = 134\] slant height of frustum,

*l*=

\[\sqrt{{1223}^2 + 1234 {}^2}\text{ textcolor} {\text{ white} }{}\]

\[ = 1234 cm\]

_{1 }+ r

_{2})

*l*

\[ = 123 sq . cm .\]

#### Pages 154 - 155

Radius of a circle is 10 cm. Measure of an arc of the crcleis 54^{°}. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

Measure of an arc of a circle is 80 cm and its radius is 18 cm. Find the length of the arc. ( \[\pi\] = 3.14 )

Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.

Radius of a circle is 10 cm. Area of a sector of the sector is 100 cm^{2} . Find the area of its corresponding major sector. ( \[\pi\] = 3.14 )

Area of a sector of a circle of radius 15 cm is 30 cm^{2} . Find the length of the arc of the sector.

*m*( arc MBN) = 60

^{°},

*m*( arc MBN) = 60

^{°},

*m*( arc MBN) = 60

^{°},

In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

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. ( \[\pi = \frac{22}{7}\])

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

Radius of a sector of a circle is 7 cm. If measure of arc of the sector is -

(2) 210^{°} find the area of the sector

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* .

#### Pages 159 - 160

In the given figure, A is the centre of the circle. \[\angle\]ABC = 45^{° }and AC = 7 \[\sqrt{2}\]cm. Find the area of segment BXC.

In the given figure, O is the centre of the circle.* m* ( arc PQR) = 60^{° }OP = 10 cm. Find the area of the shaded region.( \[\pi\]= 3.14, \[\sqrt{3}\]= 1.73)

In the given figure, if A is the centre of the circle. \[\angle\] PAR = 30^{°}, AP = 7.5, find the area of the segment PQR ( \[\pi\] = 3.14)

In the given figure, if O is the centre of the circle, PQ is a chord. \[\angle\] POQ = 90^{°}, area of shaded region is 114 cm^{2} , find the radius of the circle. \[\pi\] = 3.14)

A chord PQ of a circle with radius 15 cm subtends an angle of 60^{°} with the centre of the circle. Find the area of the minor as well as the major segment. ( \[\pi\] = 3.14, \[\sqrt{3}\] = 1.73)

#### Pages 160 - 163

(A) \[14\pi\]

(B) \[\frac{7}{\pi}\]

(C) 7\[\pi\]

(D) \[\frac{14}{\pi}\]

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

(A) 66 cm

(B) 44 cm

(C) 160 cm

(D) 99 cm

Choose the correct alternative answer for each of the following questions.

(3) Find the perimeter of a sector of a circle if its measure is 90^{°} and radius is 7 cm .

(A) 44 cm

(B) 25 cm

(C) 36 cm

(D) 56 cm

Choose the correct alternative answer for each of the following questions.

(A) 440 cm^{2 }

(B) 550 cm^{2}

(C) 330 cm^{2 }

(D) 110 cm^{2 }

Choose the correct alternative answer for each of the following questions.

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

(A) \[\frac{44}{\pi}\] cm

(B) 22 \[\pi\] CM

(C) 44 \[\pi\] CM

(D) \[\frac{22}{\pi}\] cm

Choose the correct alternative answer for each of the following questions

(6) 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.

(A) 15 cm

(B) 10 cm

(C) 18 cm

(D) 5 cm

Choose the correct alternative answer for each of the following questions

(A) 1 cm^{3}

B) 0.001 cm^{3 }

(C) 0.0001 cm^{3}

(D) 0.000001 cm^{3}

Choose the correct alternative answer for each of the following questions

^{3 }.

(A) 1 cm

(B) 10 cm

(C) 100 cm

(D)1000 cm

A washing tub in the shape of a frustum of a cone has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub ? ( \[\pi = \frac{22}{7}\])

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm , 90 cm and 30 cm respectively. How many balls were melted to make the tube?

A metal parallelopiped of measures 16 cm x 11 cm x 10 cm was melted to make coins. How many coins were made if the thickness and diameter of each coin was 2 mm and 2 cm respectively ?

The diameter and length of a roller is 120 cm and 84 cm respectively. To level the ground, 200 rotations of the roller are required. Find the expenditure to level the ground at the rate of Rs. 10 per sq.m.

The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 m respectively. The density of the metal is 8.88 gm per cm^{3 }. Find the outer surface area and mass of the sphere.

A cylindrical bucket of diameter 28 cm and height 20 cm was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was 14 cm, what was the base area of the cone ?

The area of a sector of a circle of 6 cm radius is 15 \[\pi\] sq.cm. Find the measure of the arc and length of the arc corresponding to the sector.

In the given figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion. ( \[\pi\] = 3.14, \[\sqrt{3}\]= 1.73 )

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

In the given figure , two circles with centres O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles.

#### Balbharati SSC Class 10 Mathematics 2

#### Textbook solutions for Class 10th Board Exam

## Balbharati solutions for Class 10th Board Exam Geometry chapter 7 - Mensuration

Balbharati solutions for Class 10th Board Exam Geometry chapter 7 (Mensuration) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Textbook for SSC Class 10 Mathematics 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10th Board Exam Geometry chapter 7 Mensuration are Length of an Arc, Conversion of Solid from One Shape to Another, Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle, Perimeter and Area of a Circle, Surface Area of a Combination of Solids, Euler's Formula, Areas of Sector and Segment of a Circle, Frustum of a Cone, Introduction of Surface Areas and Volumes.

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