Surface Areas and Volumes quiz

The volume of a hemisphere of radius r is:

The total surface area of a hemisphere of radius 7 cm is:

A capsule is a combination of:

The slant height of a cone of radius 6 cm and height 8 cm is:

A cone and a cylinder have the same base radius and the same height. The ratio of their volumes is:

The surface area of a sphere of radius 3.5 cm is:

Two cubes of edge 5 cm are joined end to end. The surface area of the cuboid formed is:

A solid formed by a cone on a hemisphere of equal radius r has total surface area:

The volume of a cylinder of radius 7 cm and height 10 cm is:

If the radius of a sphere is doubled, its volume becomes:

Find the curved surface area of a cone of radius 7 cm and slant height 10 cm. (Use pi = 22/7) (2 marks)

A solid is in the shape of a cone standing on a hemisphere with both their radii equal to 1 cm and the height of the cone equal to its radius. Find the volume of the solid in terms of pi. (2 marks)

Find the volume of a sphere of diameter 6 cm. (Use pi = 3.14) (2 marks)

A cylindrical glass has an inner diameter of 5 cm, but the bottom has a hemispherical raised portion of the same radius, which reduces its capacity. If the height of the glass is 10 cm, find its apparent capacity. (Use pi = 3.14) (2 marks)

For the glass in Q14, find its actual capacity. (Use pi = 3.14) (2 marks)

A cone of height 24 cm and radius 7 cm is made of modelling clay. Find its volume. (Use pi = 22/7) (2 marks)

How many litres of water can a cylindrical tank of radius 1.4 m and height 2 m hold? (Use pi = 22/7) (2 marks)

Find the total surface area of a hemisphere of diameter 21 cm. (Use pi = 22/7) (2 marks)

A juice seller serves juice in a cylindrical glass of diameter 7 cm with a hemispherical bottom raised inside. Explain with reasons why the customer gets less juice than the glass appears to hold. (2 marks)

A solid metallic sphere and a solid metallic cube have the same volume. Name two other quantities you would need to compare their surface areas. (2 marks)

Gulab jamuns contain sugar syrup up to about 30% of their volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends of length 5 cm and diameter 2.8 cm. (Use pi = 22/7) (3 marks)

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm^3 of iron has approximately 8 g mass. (Use pi = 3.14) (3 marks)

A spherical glass vessel has a cylindrical neck 8 cm long and 2 cm in diameter; the diameter of the spherical part is 8.5 cm. Find the quantity of water it can hold. (Use pi = 3.14) (3 marks)

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 bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. (Use pi = 22/7) (3 marks)

A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the height of the building if it contains 67 1/21 m^3 of air. (Use pi = 22/7) (3 marks)

Read the passage and answer the questions. A juice stall sells mango juice in glasses shaped like cylinders with a hemispherical raised bottom. Each glass has an inner diameter of 5 cm and a height of 10 cm. The stall owner advertises each glass as holding about 196 mL. (i) Find the apparent capacity of the glass. (Use pi = 3.14) (ii) Find the volume of the hemispherical raised portion. (iii) Find the actual capacity, and comment on the owner's claim. (1 cm^3 = 1 mL) (5 marks)

Read the passage and answer the questions. A circus tent is cylindrical up to a height of 3 m and conical above it. The diameter of the base is 105 m and the slant height of the conical part is 53 m. The organisers want to buy canvas to make the tent. (i) Find the curved surface area of the cylindrical part. (Use pi = 22/7) (ii) Find the curved surface area of the conical part. (iii) Find the total canvas required and the cost at Rs 100 per m^2. (5 marks)

Read the passage and answer the questions. A company makes ice-cream cones with a hemisphere of ice-cream on top. The cone has radius 3.5 cm and height 12 cm, and it is completely filled with ice-cream, with a hemispherical scoop on top. (i) Find the volume of the cone. (Use pi = 22/7) (ii) Find the volume of the hemispherical top. (iii) Find the total volume of ice-cream in one cone and in a box of 10 such cones. (5 marks)

Read the passage and answer the questions. A school orders medicine capsules for its first-aid kit. Each capsule is a cylinder with two hemispherical ends; the whole capsule is 14 mm long and 5 mm in diameter. (i) Find the length of the cylindrical part. (ii) Find the surface area of the capsule. (Use pi = 22/7) (iii) Find the volume of medicine in a capsule. (Use pi = 22/7) (5 marks)

Read the passage and answer the questions. A farmer builds a grain storage bin in the shape of a cylinder of radius 2.1 m and height 6 m with a conical roof of height 2.8 m on top. (i) Find the slant height of the conical roof. (ii) Find the volume of grain the bin can store if filled completely. (Use pi = 22/7) (iii) Find the area of metal sheet needed for the curved walls and the roof (excluding the floor). (5 marks)

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Draw a labelled sketch, and find the total surface area and the volume of the toy. (Use pi = 22/7) (6 marks)

Draw a sketch of a solid formed by a cylinder of radius 7 cm and height 20 cm with a cone of the same radius and height 24 cm on one end and a hemisphere of the same radius on the other. Find the total surface area and the volume of the solid. (Use pi = 22/7) (6 marks)

A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is 26 cm, the height of the conical part is 6 cm, and the base of the cone and the cylinder both have diameter 5 cm. Draw the figure, and find the area to be painted orange (cone) and yellow (cylinder), assuming the base of the cylinder is also painted yellow. (Use pi = 3.14) (6 marks)

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 the heap? Draw a sketch and explain why the base area is not included. (Use pi = 3.14) (6 marks)

Explain, with sketches, how to find the surface area and volume of (i) a cylinder with a hemisphere scooped out from one end (ii) a cuboid with a cylindrical hole drilled through it. Then find the volume and total surface area for (i) when the cylinder has radius 7 cm and height 15 cm. (Use pi = 22/7) (6 marks)