Surface Area and Volume Quiz

A rectangular piece of paper measuring 11 cm by 8 cm can be exactly wrapped to cover the curved surface of a cylinder of height 8 cm. What is the volume of the cylinder?

1. 81 cm3
2. 77 cm3
3. 70 cm3
4. 27 cm3

Answer: (b) 77 cm3

Find the percentage increase in the area of the triangle if each of its side is doubled.

1. 800%
2. 100%
3. 300%
4. 50%

Answer: (c) 300%

ACB is an arc of a circle of radius 3 cm. It subtends an angle of 120o at the centre, as shown in the figure. What is an area of the shaded portion ACB?

1. (3π - 9√(3)/4) cm2
2. (π - 9√(3)/4) cm2
3. (3π - 3√(3)/4) cm2
4. (2π - 9√(3)/4) cm2

Answer: (a) (3π - 9√(3)/4) cm2

The length of the hypotenuse of a right-angled triangle is 13 cm, and its area is 30 cm2. Find the lengths of the remaining two sides.

1. 12 cm, 6 cm
2. 11 cm, 10 cm
3. 6 cm, 8 cm
4. 5 cm, 12 cm

Answer: (d) 5 cm, 12 cm

In a right-angled triangle ABC, D is the foot of the perpendicular from B on the hypotenuse AC. If AB = 3 cm and BC = 4 cm, what is the area of ΔABD?

1. 11/56 cm2
2. 54/25 cm2
3. 11/26 cm2
4. 21/65 cm2

Answer: (b) 54/25 cm2

A circle is inscribed in an equilateral triangle of side a cm. What is the area of any square inscribed in this circle?

1. a2/3 cm2
2. a3/8 cm2
3. a2/6 cm2
4. a2/8 cm2

Answer: (c) a2/6 cm2

A sphere and a cube have the same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube?

1. 6 : π
2. 6 : 5π
3. 6π : 1
4. π : 5

Answer: (a) 6 : π

In a circular sheet of perimeter 2πr touching each side of a given quadrilateral sheet of perimeter 2p is cut off from the quadrilateral, then what is the area of the remaining sheet?

1. pr square units
2. r(p - πr) square units
3. πr square units
4. r2 square units

Answer: (b) r(p - πr) square units

Read the following passage and answer the following question: ABCD is a square with a side length of a cm. The sides AB, BC, CD, and AD are all chords of circles, each with the same radius. Each chord subtends an angle of 120° at the centre of its corresponding circle. Calculate the total area of the figure formed by the square and the four arcs.

1. (a2 + 5a2(1 + 4(π/9 + √3/4)) square units
2. (a2 + 4a2(1 - 4(π/9 - √3/4)) square units
3. (a + 4a(1 + 4(π/9 - √3/4)) square units
4. a2(1 + 4(π/9 - √3/4) square units

Answer: (d) a2(1 + 4(π/9 - √3/4) square units

Read the following passage and answer the following question: ABCD is a square with the side length of a cm. The sides AB, BC, CD, and AD are all chords of circles, each with the same radius. Each chord subtends an angle of 120° at the centre of its corresponding circle. Find the volume of a cylindrical structure constructed by extruding this figure vertically by a height h.

1. (a2(1 - 4h(π/9 - √3/4)) square units
2. (a2h(1 + 4(π/9 - √3/4)) square units
3. (a2(1 + 4(π/9 - √3/4)h)) square units
4. (ah(1 - 4(π/9 - √3/4)) square units

Answer: (b) (a2h(1 + 4(π/9 - √3/4)) square units