Class 10 - Chapter 12: Surface Areas and Volumes

Section A (1 Mark each)

Q1. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. The volume of the solid is:

(a) $\pi$ cm$^3$ (b) $2\pi$ cm$^3$ (c) $\frac{2}{3}\pi$ cm$^3$ (d) $\frac{4}{3}\pi$ cm$^3$

Q2. The total surface area of a solid hemisphere of radius $r$ is:

(a) $2\pi r^2$ (b) $3\pi r^2$ (c) $4\pi r^2$ (d) $\pi r^2$

Q3. A surahi is the combination of:

(a) a sphere and a cylinder (b) a hemisphere and a cylinder (c) two hemispheres (d) a cylinder and a cone

Q4. Assertion (A): If two cubes of edge 5 cm are joined end to end, the surface area of the resulting cuboid is 250 cm$^2$.
Reason (R): The total surface area of a cuboid of dimensions $l, b, h$ is $2(lb + bh + hl)$.

(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. Two cubes each of volume 64 cm$^3$ are joined end to end. Find the surface area of the resulting cuboid.

Solve on white paper.

Q6. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Solve on white paper.

Q7. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Solve on white paper.

Section C (3 Marks each)

Q8. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m$^2$.

Solve on white paper.

Q9. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Solve on white paper.

Section D (5 Marks)

Q10. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm$^2$.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Gulab Jamun

A gulab jamun contains sugar syrup up to about 30% of its volume. Each gulab jamun is shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

(i) Find the radius of the cylindrical part.

(ii) Find the length of the cylindrical part.

(iii) Find the volume of one gulab jamun.

Solve on white paper.