OCR GCSE Maths: Perimeter, Area and Volume

A stained-glass window has the shape of a rectangle with a semicircle on top. The rectangular part is $120$120 cm wide and $200$200 cm tall. The semicircle is attached to the top edge of the rectangle, so its diameter is the same as the width of the rectangle, $120$120 cm. The flat bottom edge of the window is one of the $120$120 cm sides; the two $200$200 cm sides are vertical.

(a) Work out the total perimeter of the window. Give your answer to $3$3 significant figures. (2 marks)

(b) Work out the total area of the glass in the window. Give your answer to $3$3 significant figures. (2 marks)

(c) Using your area from part (b), work out the area of the glass in $\text{m}^2$m2, giving your answer to $3$3 significant figures. (1 mark)

[Circumference of a circle $= 2\pi r$=2πr. Area of a circle $= \pi r^2$=πr2.]

A sector of a circle has radius $12$12 cm and an angle of $150^{\circ}$150∘ at the centre.

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

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

A water butt is in the shape of a solid cylinder with radius $20$20 cm and height $50$50 cm.

(a) Work out the volume of the cylinder. Give your answer in $\text{cm}^3$cm3 to $3$3 significant figures. (2 marks)

(b) The water butt is filled completely with water. Given that $1$1 litre $= 1000 \text{ cm}^3$=1000 cm3, work out the capacity of the water butt in litres. Give your answer to $3$3 significant figures. (2 marks)

[Volume of a cylinder $= \pi r^2 h$=πr2h.]

A solid metal ball bearing is a sphere with radius $3$3 cm.

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

(b) Hence write down the volume to $3$3 significant figures. (1 mark)

[Volume of a sphere $= \tfrac{4}{3}\pi r^3$=34​πr3.]

A trapezium has two parallel sides of length $8$8 cm and $14$14 cm. The perpendicular distance between the parallel sides is $5$5 cm. Work out the area of the trapezium. (2 marks)

[Area of a trapezium $= \tfrac12(a + b)h$=21​(a+b)h.]

A triangle has a base of length $9$9 cm and a perpendicular height of $6$6 cm. Work out the area of the triangle. (1 mark)