Class 10 - Chapter 12: Surface Areas and Volumes

Section A (1 Mark each)

Q1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. The height of the cylinder is:

(a) 2.74 cm (b) 3.14 cm (c) 4.2 cm (d) 1.4 cm

Q2. Three metallic solid spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The radius of the resulting sphere is:

(a) 6 cm (b) 8 cm (c) 12 cm (d) 10 cm

Q3. During conversion of a solid from one shape to another, the volume of the new shape will:

(a) increase (b) decrease (c) remain unaltered (d) be doubled

Q4. Assertion (A): The number of spherical balls of radius 1 cm that can be made from a solid sphere of radius 4 cm is 64.
Reason (R): The volume of the big sphere is equal to $n$ times the volume of the small sphere.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Solve on white paper.

Q6. A metallic sphere of radius 6 cm is melted and recast into a wire of diameter 2 mm. Find the length of the wire.

Solve on white paper.

Q7. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5 \text{ cm} \times 10 \text{ cm} \times 3.5 \text{ cm}$?

Solve on white paper.

Section C (3 Marks each)

Q8. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Solve on white paper.

Q9. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Solve on white paper.

Section D (5 Marks)

Q10. A cylindrical bucket, 32 cm high and with radius of base 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 heap is 24 cm, find the radius and slant height of the heap.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Rainwater Harvesting

Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions $1.57 \text{ m} \times 1.44 \text{ m} \times 95 \text{ cm}$. The overhead tank has its radius 60 cm and height 95 cm. (Use $\pi = 3.14$)

(i) Find the volume of the sump.

(ii) Find the volume of the overhead tank.

(iii) Compare the capacity of the tank with that of the sump (Ratio of Tank to Sump).

Solve on white paper.