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## Chapter 7: Mensuration

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 7 Mensuration Practice set 7.1 [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. The 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 are 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.

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 7 Mensuration Practice set 7.2 [Page 148]

^{3 })

The radii of the ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its 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 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 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.( \[\pi = \frac{22}{7}\])

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 7 Mensuration Practice set 7.3 [Pages 154 - 155]

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

The measure of an arc of a circle is 80° and its radius is 18 cm. Find the length of the arc. (π = 3.14)

The 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.

The radius of a circle is 10 cm. The 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.

^{°},

^{°},

^{°},

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 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.

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.

(2) Area of any one of the sectors

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 7 Mensuration Practice set 7.4 [Pages 159 - 160]

In the given figure, A is the centre of the circle. ∠ABC = 45^{° }and AC = 7√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 center of the circle, PQ is a chord. \[\angle\] POQ = 90^{°}, area of the shaded region is 114 cm^{2}, find the radius of the circle. \[\pi\] = 3.14)

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

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 7 Mensuration Practice set 7.4 [Pages 160 - 163]

\[14\pi\]

\[\frac{7}{\pi}\]

7\[\pi\]

\[\frac{14}{\pi}\]

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

66 cm

44 cm

160 cm

99 cm

Choose the correct alternative answer for the following question.

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

44 cm

25 cm

36 cm

56 cm

Choose the correct alternative answer for the following question.

440 cm

^{2 }550 cm

^{2}330 cm

^{2 }110 cm

^{2 }

**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.

`44/pi` cm

22 \[\pi\] CM

44 \[\pi\] CM

\[\frac{22}{\pi}\] cm

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.

15 cm

10 cm

18 cm

5 cm

Choose the correct alternative answer for the following question.

1 cm

^{3}0.001 cm

^{3 }0.0001 cm

^{3}0.000001 cm

^{3}

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

^{3}.

1 cm

10 cm

100 cm

1000 cm

A washing tub in the shape of a frustum of a cone has a height of 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 were 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 a height of 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.

## Chapter 7: Mensuration

## Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board chapter 7 - Mensuration

Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board 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 Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board chapter 7 Mensuration are Conversion of Solid from One Shape to Another, Concept of Surface Area, Volume, and Capacity, Frustum of a Cone, Length of an Arc, Euler's Formula, Circumference of a Circle, Areas of Sector and Segment of a Circle, Surface Area and Volume of Three Dimensional Figures, Surface Area and Volume of Different Combination of Solid Figures, Sector of a Circle, Area of a Sector of a Circle, Segment of a Circle, Area of a Segment.

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