A cone of maximum volume is carved out of a block of wood of size 20 cm × 10 cm × 10 cm . Find the volume of the remaining wood.

Given : Size of the wooden block = 20 cm × 10 cm × 10 cm Maximum diameter of the cone = 10 cm Height h of the cone = 20 cm ∴ Radius r of the cone 10 2 = 5 cm We know that, volume of the cuboid is l b h . Now, Volume of the block = 20 × 10 × 10 = 2000 cm 3 And, Volume of cone = 1 3 πr 2 h = 1 3 × 22 7 × 5 × 5 × 20 = 11000 21 cm 3 ∴ Volume of the remaining portion is equals to the difference of volume of cuboid and the volume of cone. = 2000 - 11000 21 = 42000 - 11000 21 = 31000 21 ≈ 1476 . 19 cm 3 Hence, the volume of the remaining solid is 1476 . 19 cm 3 .

16 glass spheres each of radius 2 cm are packed in a cubiodal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of the water filled in the box.

Given, dimensions of the cuboidal box = 16 cm × 8 cm × 8 cm We know that volume of the cuboid is l b h ∴ Volume of the cuboidal box = 16 × 8 × 8 = 1024 cm 3 Also, given radius of one glass sphere = 2 cm ∴ Volume of one glass sphere = 4 3 πr 3 = 4 3 × 22 7 × 2 3 = 704 21 = 33 . 523 cm 3 Now, volume of 16 glass spheres 16 × 33 . 253 = 536 . 37 cm 3 ∴ Required volume of water = Volume of cuboidal - Volume of 16 glass spheres = 1024 - 536 . 37 = 487 . 6 cm 3 Hence, the required water volume is 487 . 6 cm 3

A solid metallic sphere of radius 6 c m is melted and made into a solid cylinder of height 32 c m . Find the curved surface area of the cylinder. (Take π = 3 . 1 )

Radius of metallic sphere R = 6 c m Height of cylinder h = 32 c m Volume of cylinder = Volume of metallic sphere π r 2 h = 4 3 π R 3 r 2 × 32 = 4 3 × 6 3 r 2 = 4 × 6 × 6 × 6 3 × 32 r 2 = 9 r = 3 c m Then, curved surface area of the cylinder = 2 π r h = 2 × 3 . 1 × 3 × 32 = 595 . 2 c m 2

E M B I B E

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.3>Q 12

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IMPORTANT

Earn 100

A hemispherical bowl has a radius of $3.5 cm$ . What would be the volume of water it would contain?

Important Questions on Mensuration

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.3>Q 13

The surface area of a solid sphere is

1256 {cm}^{2}

. It is cut into two hemispheres. Find the total surface area and the volume of a hemisphere. Take

π = 3.14

.

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IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 1

The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 2

The adjoining figure shows a solid trophy made of shinning glass. If one cubic centimetre of glass costs $₹ 0.75$ , find the cost of the glass for making the trophy.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 3

From a cube of edge

14 cm

, a cone of maximum size is carved out. Find the volume of the remaining material.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 4

A cone of maximum volume is carved out of a block of wood of size

20 cm \times 10 cm \times 10 cm

. Find the volume of the remaining wood.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 5

16

glass spheres each of radius

2 cm

are packed in a cubiodal box of internal dimensions

16 cm \times 8 cm \times 8 cm

and then the box is filled with water. Find the volume of the water filled in the box.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 6

A cubical block of side

7 cm

is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also find the surface area of the solid.

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Understanding ICSE Mathematics Class 10>Chapter 17 - Mensuration>Exercise 17.4>Q 7

A hemispherical and conical hole are scooped out of a solid wooden cylinder. Find the volume of the remaining solid where measurements are as follows:

The height of the cylinder is $7 cm$ , radius of each hemisphere, cone and cylinder is $3 cm$ . Height of cone is $3 cm$ . Give your answer correct to the nearest whole number. Take $π = \frac{22}{7}$ .