AQA GCSE Maths: Perimeter, Area and Volume

A solid cone has base radius $5$5 cm and slant height $13$13 cm.

(a) Show that the vertical height of the cone is $12$12 cm. (2 marks)

(b) Work out the volume of the cone. Give your answer as an exact multiple of $\pi$π. (2 marks)

(c) Work out the total surface area of the cone (curved surface plus base). Give your answer as an exact multiple of $\pi$π. (1 mark)

[Volume of a cone $= \tfrac{1}{3}\pi r^2 h$=31​πr2h. Curved surface area of a cone $= \pi r l$=πrl.]

A sector of a circle has radius $9$9 cm and an angle of $80^{\circ}$80∘ at the centre.

(a) Work out the arc length of the sector, giving your answer to $3$3 significant figures. (2 marks)

(b) Work out the area of the sector, giving your answer to $3$3 significant figures. (2 marks)

Two solid spheres are mathematically similar. The smaller sphere has radius $4$4 cm and the larger sphere has radius $6$6 cm.

(a) The surface area of the smaller sphere is $64\pi \text{ cm}^2$64π cm2. Work out the surface area of the larger sphere, as a multiple of $\pi$π. (2 marks)

(b) The volume of the larger sphere is $288\pi \text{ cm}^3$288π cm3. Work out the volume of the smaller sphere, as a multiple of $\pi$π. (2 marks)

A solid cylinder has radius $4$4 cm and height $10$10 cm.

(a) Work out the volume of the cylinder, giving your answer to $3$3 significant figures. (2 marks)

(b) Work out the total surface area of the cylinder, giving your answer to $3$3 significant figures. (1 mark)

A trapezium has parallel sides of length $7$7 cm and $11$11 cm, and the perpendicular distance between them is $6$6 cm. Work out the area of the trapezium. (2 marks)

Work out the circumference of a circle with radius $7$7 cm. Give your answer to $3$3 significant figures. (1 mark)