Edexcel GCSE Maths: Perimeter, Area and Volume

A solid is made from a hemisphere joined to a cylinder. The cylinder has radius $5$5 cm and height $14$14 cm. The hemisphere has radius $5$5 cm and sits exactly on top of the cylinder.

(a) Work out the total volume of the solid. Give your answer in terms of $\pi$π. (3 marks)

(b) Hence work out the total volume correct to 3 significant figures. (2 marks)

(Volume of a sphere $= \frac{4}{3}\pi r^3$=34​πr3.)

A sector of a circle has radius $9$9 cm and angle $40^{\circ}$40∘ at the centre.

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

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

A trapezium has parallel sides of length $12$12 cm and $7$7 cm. The perpendicular distance between the parallel sides is $h$h cm. The area of the trapezium is $66\ \text{cm}^2$66 cm2.

(a) Work out the value of $h$h. (3 marks)

(b) Write down the formula you used, in the form area $= \dfrac{1}{2}(a + b)h$=21​(a+b)h. (1 mark)

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

Work out the total surface area of the cylinder, giving your answer in terms of $\pi$π. (3 marks)

A circle has a circumference of $31.4$31.4 cm.

Work out the radius of the circle. Use $\pi = 3.14$π=3.14 and give your answer correct to 3 significant figures. (2 marks)

A triangle has base $14$14 cm and perpendicular height $6$6 cm.

Work out the area of the triangle. (1 mark)