Sec 2 Mathematics Pyramids, Cones & Spheres topical questions

A pyramid stands on a rectangular base of 5 cm by 8 cm, with a vertical height of 9 cm.

1. (a)Find the area of the base.[1]
2. (b)Find the volume of the pyramid.[2]

A cone has radius 6 and vertical height 10. Take pi as 3.14.

1. (a)Find the volume of the cone.[2]
2. (b)Round your answer to the nearest whole number.[1]

A sphere has radius 3. Take pi as 3.14.

1. (a)Find the volume of the sphere.[2]
2. (b)Find the surface area of the sphere.[1]

A pyramid stands on a triangular base of area 30 cm², with a vertical height of 14 cm.

1. (a)Write the volume formula with the numbers substituted.[1]
2. (b)Find the volume.[1]

A cone has radius 9 and vertical height 12. Take pi as 3.14.

1. (a)Find the slant height.[1]
2. (b)Find the volume of the cone, correct to 2 decimal places.[2]

A cone has radius 8 and vertical height 15. Take pi as 3.14.

1. (a)Find the slant height of the cone.[2]
2. (b)Find the curved surface area.[2]

A square pyramid has a base edge of 10 and a vertical height of 12.

1. (a)Find the volume of the pyramid.[2]
2. (b)Find the height of each triangular face (its slant height).[1]
3. (c)Find the total surface area including the base.[1]

A silo is built from a cylinder of radius 5 and height 8, topped by a hemisphere of radius 5. Take pi as 3.14.

1. (a)Find the volume of the cylinder part.[1]
2. (b)Find the volume of the hemisphere part.[2]
3. (c)Find the total volume, correct to 2 decimal places.[1]

A conical tank has radius 21 and height 30. Take pi as 22/7.

1. (a)Find the tank’s volume in cm³.[2]
2. (b)Convert your answer to litres.[2]

A sphere has radius 21. Take pi as 22/7.

1. (a)Find the surface area of the sphere.[2]
2. (b)Find the volume of the sphere.[2]

A conical sand pile has radius 3 m and vertical height 4 m. Take pi as 3.14.

1. (a)Find the volume of sand, correct to 2 decimal places.[2]
2. (b)A lorry carries 6 m³ per trip. How many full trips are needed to remove all the sand?[2]

A metal sphere of radius 6 is melted down and recast into a cone with base radius 6. Take pi as 3.14.

1. (a)Find the volume of the sphere.[2]
2. (b)State the volume of the recast cone, with a reason.[1]
3. (c)Find the cone’s height, correct to 2 decimal places.[2]

A cube of edge 12 contains a sphere of diameter 12 that just touches every face. Take pi as 22/7.

1. (a)Find the volume of the cube.[1]
2. (b)Find the volume of the sphere.[2]
3. (c)What percentage of the cube’s volume does the sphere fill? Correct to 1 decimal place.[2]

A paper cup is a cone with radius 3 and height 7. Take pi as 22/7.

1. (a)Find the volume of one cup.[2]
2. (b)A jug holds 4.62 litres of juice. How many full cups can be poured?[2]
3. (c)State one assumption behind your answer to part (b).[1]

A toy spinning top is a cone (radius 6, height 8) sitting exactly on a hemisphere (radius 6). Take pi as 3.14.

1. (a)Find the volume of the cone part.[1]
2. (b)Find the volume of the hemisphere part.[1]
3. (c)Find the total volume of the top.[1]
4. (d)Find the slant height of the cone part.[1]
5. (e)Explain why the slant height is not needed for part (c).[1]