Surface, Area and Volume

The base of a right pyramid is an equilateral triangle each side of 4 cm long and the skant edge is 5 cm long. Find the volume of the pyramid.

1. (24√5)/3 m3
2. (4√59)/3 m3
3. 21√5/7 m3
4. 11√5 m3

Answer: (b) (4√59)/3 m3

A toy is in the form of a cone mounted on a hemispehere such that the diameter of the base of the cone is equal to that of the hemisphere. If the diameter of the base of the cone is 6 cm and its height is 4 cm, what is the surface area of the toy?

1. 102.93 cm2
2. 125.62 cm2
3. 115.25 cm2
4. 103.62 cm2

Answer: (d) 103.62 cm2

Consider a regular hexagon with each side measuring 'a' units. If a square is inscribed such that it shares an edge with two non-adjacent sides of the hexagon, find the area of the square in terms of 'a'.

1. √3a2 square units
2. 3a square units
3. 3a2 square units
4. 5a2 square units

Answer: (c) 3a2 square units

A container is in the form of a right circular cylinder surmounted by a hemisphere of the same radius of 15 cm as the cylinder. If the volume of the container is 32400 π cm3, then the height h of the container satisfies which one of the following?

1. 125 < h < 135 cm
2. 135 < h < 149 cm
3. 115 < h < 120 cm
4. 100 < h < 110 cm

Answer: (b) 135 < h < 149 cm

A square hole of cross-sectional area 4 cm2 is drilled across a cube with its length parallel to the side of the cube. If an edge of the cube measures 5 cm, what is the total surface area of the body so formed?

1. 95 cm2
2. 105 cm2
3. 115 cm2
4. 182 cm2

Answer: (d) 182 cm2

A cylindrical tank with a diameter of 24 cm is partially filled with water. A solid spherical ball with a radius of 6 cm is completely immersed in the tank. Calculate the rise in the water level in the tank after the ball is immersed.

1. 2 cm
2. 5 cm
3. 11 cm
4. 10 cm

Answer: (a) 2 cm

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm (π = 3.14)?

1. 1.24 m3
2. 1.42 m3
3. 1.31 m3
4. 1.13 m3

Answer: (d) 1.13 m3

Read the passage and answer the following question. In some countries, traditional festivals like Diwali, Christmas, or Eid bring people together in vibrant community gatherings. At religious festivals, a stall owner has a large cylindrical tank with a base radius of 20 cm and a height of 50 cm, filled to the brim with lassi (a yoghurt-based drink). He pours the lassi into cone-shaped cups, each with a radius of 4 cm and a height of 10 cm. These cups are sold for $20 each. The stall features decorations made of hollow spherical ornaments with an outer radius of 6 cm and an inner radius of 5 cm, hanging at the counter. What is the volume of Lassi?

1. 12456π cm3
2. 20000π cm3
3. 20150π cm3
4. 11005π cm3

Answer: (b) 20000π cm3

Each height and side of the base of a regular hexagonal pyramid is equal to x cm. Find its lateral surface area in terms of x (in cm2).

1. 3√7x2/2
2. 7√7x2/2
3. 5√7x2/2
4. 2√2x2/2

Answer: (a) 3√7x2/2

Find the volume of a tetrahedron the sides of whose base are 9 cm, 12 cm and 15 cm and whose height is 15 cm.

1. 200 cm3
2. 225 cm3
3. 270 cm3
4. 360 cm3

Answer: (c) 270 cm3