Worksheets · Foundation and Higher

Pyramids, cones, spheres and composite solids

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Calculator · 2 marks

   A sphere has a radius of 6 cm. Volume of a sphere $= \frac{4}{3}\pi r^3$, where $r$ is the radius.

   (a) Work out the volume of the sphere. Give your answer correct to 3 significant figures. (2)
2. Question 2Calculator · 5 marks

   A solid cone has base radius 5 cm, perpendicular height 12 cm and slant height 13 cm. Curved surface area of a cone $= \pi r l$, where $l$ is the slant height. Volume of a cone $= \frac{1}{3}\pi r^2 h$.

   (a) Work out the volume of the cone. Give your answer correct to 3 significant figures. (2)

   (b) Work out the total surface area of the cone. Give your answer correct to 3 significant figures. (3)
3. Question 3Non-calculator · 4 marks

   (a) A paper sector has radius 15 cm and angle $216^\circ.$ Its two straight edges are joined without overlap to form the curved surface of a cone. Work out the volume enclosed by the cone. Give your answer in terms of $\pi .$ Volume of a cone $= \frac{1}{3}\pi r^2 h$ You must show your working. (4)