Spheres
A sphere has a radius of 5 cm. Find its volume, correct to 3 significant figures.
524 cm³
A solid hemisphere has a radius of 12.5 cm. Find its total surface area, including the circular base. Give your answer correct to 3 significant figures.
1470 cm²
A cone has a radius of 5 cm and a perpendicular height of 12 cm. Find its volume.
314 cm³
A cone has a radius of 4 cm and a height of 6 cm. What is its volume?
101cm3
A student says:
“The volume of a cone is V=πr2h.
Is the student correct? If not, state the correct formula.
1/3πr2h.
A spherical ball has a diameter of 18 cm. Find its surface area, correct to 3 significant figures.
1,020 cm²
A hemisphere has a volume of 4500 cm³. Find its radius. Give your answer correct to 3 significant figures.
12.9 cm
A cone has a radius of 7 cm and a slant height of 15 cm. Find its curved surface area.
330 cm²
Which measurement is needed to calculate the curved surface area of a cone?
A. Radius
B. Diameter
C. Slant height
D. Vertical height
C
A student is finding the total surface area of a square-based pyramid. They calculate only the areas of the 4 triangular faces.
What did the student forget?
The base of the pyramid.
A spherical water tank has a radius of 12 cm. It is filled to 75% of its capacity. Find the volume of water in the tank, correct to 3 significant figures.
5,430 cm³
A hemispherical bowl has a curved surface area of 850 cm². Find its volume. Give your answer correct to 3 significant figures.
3300 cm³
A cone has a radius of 6 cm and a perpendicular height of 8 cm. Find its total surface area.
302 cm²
A cone has a diameter of 10cm and a slant height of 13 cm. Find its total surface area.
283cm2
A student is finding the volume of a pyramid and uses the slant height instead of the vertical height.
Explain why this is incorrect and state which height should be used.
The volume of a pyramid uses the vertical height, not the slant height.
A solid metal sphere has a surface area of 196π cm². Find the volume of the sphere, giving your answer correct to 3 significant figures.
1,440 cm³
A solid hemisphere has a total surface area of 1750 cm², including its circular base. Find its volume. Give your answer correct to 3 significant figures.
5300 cm³
A cone has a volume of 2145.7 cm³. Its perpendicular height is three times its radius. Find the perpendicular height, correct to 3 significant figures.
26.4 cm
A company manufactures cone-shaped containers for a new product. Each container has a volume of 400 cm³ and a diameter of 12 cm.
The company wants to cover the entire outside surface of the container, including the circular base, with a special material.
What is the total surface area of one container, correct to 3 significant figures?
344cm2
A student says:
“A sphere has a radius of 6 cm, so its surface area is 2πr2, just like the surface area of a circle.”
Is the student correct? Explain the misconception.
No. A sphere is a 3D object, so its surface area is 4πr2.
A spherical container has a diameter of 30 cm. It contains water to 4/5 of its capacity. The water is poured into a cylindrical container with a radius of 10 cm. During the transfer, 8% of the water is spilled. Find the height of the water in the cylindrical container, correct to 3 significant figures.
33.1 cm
A hemispherical container has a volume of 12,500 cm³. The radius of the hemisphere is increased by 18%. Find the new volume of the container. Give your answer correct to 3 significant figures.
20,500 cm³
A cone has a curved surface area of 251.2 cm². Its slant height is 2.5 times its radius. Find the volume of the cone, correct to 3 significant figures.
434cm
A company is designing a conical water tank. The tank has a diameter of 14 m and can hold 900 m³ of water when completely full.
The company wants to paint the entire curved surface of the tank, excluding the circular base.
Paint is sold in cans, with each can covering 50 m². The company buys 10% more paint than the amount required to account for wastage.
How many cans of paint should the company buy?
Give your answer as a whole number.
10 cans
A student is calculating the total surface area of a square-based pyramid. The pyramid has a base side length of 10 cm, a vertical height of 12 cm, and a slant height of 13 cm.
The student calculates:
Surface area=102+4(21×10×12)
They get an answer of 340 cm².
Identify the student's mistake and calculate the correct total surface area.
The student used the vertical height (12 cm) to find the area of the triangular faces.
The triangular faces require the slant height (13 cm).
Surface area=102+4(21×10×13) =100+260 360 cm2