Sec 3 E-Math Mensuration topical questions

A trapezium has parallel sides of 7 cm and 13 cm with perpendicular height 6 cm. Find its area.

A parallelogram has base 10 cm and perpendicular height 7 cm. Find its area.

Find the perimeter and area of a sector of radius 8 cm with angle 45°. (Use π = 3.14159… and give answers to 3 s.f.)

Convert (a) 45° to radians, leaving your answer in terms of π, and (b) 1.2 radians to degrees (1 d.p.).

A tank measures 1.5 m by 60 cm by 40 cm. Find its volume in cm³ and its capacity in litres.

A circle has radius 9 cm. Find (a) its circumference and (b) its area, each correct to 3 significant figures.

A water tank is a cuboid measuring 80 cm by 50 cm by 45 cm. Find its capacity in litres.

A sector has radius 9 cm and angle 120°. Find (a) its arc length and (b) its area, each to 3 significant figures.

A chord of a circle of radius 12 cm subtends 60° at the centre. Find the area of the segment, to 3 significant figures.

A cone has radius 5 cm and vertical height 12 cm. Find (a) its slant height, (b) its volume, and (c) its curved surface area, each to 3 significant figures.

1. (a)Slant height.[1]
2. (b)Volume.[2]
3. (c)Curved surface area.[2]

A square pyramid has base side 10 cm and vertical height 12 cm. Find (a) its volume and (b) its total surface area, to 3 significant figures.

A running track is a rectangle 100 m by 60 m with semicircular ends of radius 30 m. Find (a) the perimeter of the track and (b) its total area, to 3 significant figures.

1. (a)Perimeter.[2]
2. (b)Area.[3]

A sector has radius 12 cm and angle 150°. Find (a) its arc length, (b) its perimeter, and (c) its area, each correct to 3 significant figures.

A cylindrical oil drum has radius 30 cm and height 85 cm. Find (a) its capacity in litres, correct to 3 significant figures, and (b) its total surface area in cm², correct to 3 significant figures.

A solid is a cylinder of radius 4 cm and height 10 cm with a cone of the same radius and height 6 cm mounted on top. (a) Find the total volume. (b) Find the total surface area, to 3 significant figures.

1. (a)Total volume.[3]
2. (b)Total surface area.[3]

A metal sphere of radius 6 cm is melted down and recast into a cylinder of radius 4 cm. (a) Find the volume of metal. (b) Find the height of the cylinder, to 3 significant figures.

1. (a)Volume of metal.[2]
2. (b)Cylinder height.[3]

A cylindrical hole of radius 2 cm is drilled straight through a cube of side 8 cm, along its full height. (a) Find the volume of the remaining solid, to 3 significant figures. (b) Explain how the surface area changes compared with the original cube, and state the new surface area to 3 significant figures.

1. (a)Remaining volume.[3]
2. (b)New surface area.[3]

A sector of radius 10 cm and angle 1.2 radians is rolled into a cone without overlap. (a) Find the arc length of the sector. (b) Hence find the radius of the cone’s base. (c) The cone’s slant height equals the sector’s radius; find the cone’s vertical height and volume, to 3 significant figures.

1. (a)Arc length.[2]
2. (b)Base radius.[1]
3. (c)Height and volume.[3]

A spinning top is a cone of radius 6 cm and vertical height 8 cm mounted on a solid hemisphere of radius 6 cm. Find (a) its total volume and (b) its total surface area, each correct to 3 significant figures.

A sector of radius 12 cm and angle 135° is rolled into a right circular cone with no overlap. (a) Show that the base radius of the cone is 4.5 cm. (b) Find the vertical height of the cone, correct to 3 significant figures. (c) Find the volume of the cone, correct to 3 significant figures.

1. (a)Show the base radius.[2]
2. (b)Vertical height.[2]
3. (c)Volume.[2]