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

Given, dimensions of the cuboidal box = 16 cm × 8 cm × 8 cm ∴ 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

HARD

10th CBSE

IMPORTANT

Earn 100

A heap of rice is in the form of a cone of diameter $9 m$ and height $3.5 m$ . Find the volume of the rice. How much canvas cloth is required to just cover heap?

Important Questions on Surface Areas and Volumes

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 7

A factory manufactures

120000

pencils daily. The pencils are cylindrical in shape each of length

25 c m

and circumference of base as

1.5 cm

. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at

₹ 0.05 per {dm}^{2}

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 8

Water is flowing at the rate of

15 {kmh}^{- 1}

through a pipe of diameter

14 cm

into a cuboidal pond which is

50 cm

long and

44 cm

wide. In what time will the level of water in pond rise by

21 cm

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 9

A solid iron cuboidal block of dimensions $4.4 m \times 2.6 m \times 1 m$ is recast into a hollow cylindrical pipe of internal radius $30 cm$ and thickness $5 cm .$ Find the length of the pipe.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 10

$500$ persons are taking a dip into a cuboidal pond which is $80$ long and $50$ broad. What is the rise of water level in the pond, if the average displacement of the water by a person is $0.04 m^{3}$ ?

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 11

16

glass spheres each of radius

2 cm

are packed into a cuboidal box of internal dimensions

16 cm \times 8 cm \times 8 cm

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

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 12

A milk container of height

16 cm

is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as

8 cm

and

20 cm

, respectively. Find the cost of milk at the rate of

₹ 22

per

L

which the container can hold.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 13

A cylindrical bucket of height

32 cm

and base radius

18 cm

is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heat is

24 cm

, find the radius and slant height of the heap.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 12 - Surface Areas and Volumes>Exercise>Q 14

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are

6 cm

and

12 cm

, respectively. If the slant height of the conical portion is

5 cm

, then find the total surface area and volume of the rocket.

(use : π = 3.14)

A heap of rice is in the form of a cone of diameter 9m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover heap?

Important Questions on Surface Areas and Volumes

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A heap of rice is in the form of a cone of diameter $9 m$ and height $3.5 m$ . Find the volume of the rice. How much canvas cloth is required to just cover heap?