Pack A — Fluency

Mathematics

Year 9 · 9.2 Mensuration

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
A cuboid has length 8 cm, width 5 cm, height 4 cm. Find its volume.
2.
A cube has side 4 cm. Find its total surface area.
3.
A cylinder has radius 3 cm and height 10 cm. Find the volume in terms of π.
4.
A triangle base 6 cm, perpendicular height 8 cm. Find the area.
5.
A trapezium has parallel sides $a$ and $b$ , height $h$ . Find $A$ when $a = 4$ , $b = 10$ , $h = 5$ .
6.
A square pyramid has base side 6 cm and height 9 cm. Find the volume.
7.
A cone has radius 6 cm, height 12 cm. Find the volume in terms of π.
8.
A sphere has radius 3 cm. Find the volume in terms of π.
9.
A cuboid with dimensions 6 × 4 × 3 cm. Find the surface area.
10.
A cylinder has radius 4 cm and height 10 cm. Find its total surface area in terms of π (including top and bottom).

SilverQuestions 11–20

11.
A triangular prism has triangular cross-section with legs 5 and 12 (right-angled), and length 20 cm. Find the volume.
12.
A square pyramid has base side 8 cm and slant height 10 cm. Find the surface area.
13.
A sphere has radius 6 cm. Find its surface area in terms of π.
14.
Make $h$ the subject of $V = \pi r^2 h$ .
15.
A cone has volume $48\pi$ cm³ and radius 4 cm. Find its height.
16.
Find the volume of a cuboid pyramid (rectangular base) with base 6 × 4 and height 12.
17.
A cylinder has volume $200\pi$ cm³ and height 10 cm. Find its radius.
18.
A hemisphere has radius 5 cm. Find (a) volume, (b) curved surface area.
19.
A rectangular tank holds 1200 L of water. Length 2 m, width 1.5 m. Find the depth.
20.
Convert: a tank holds 250 L. Find its volume in (a) m³ and (b) cm³.

GoldQuestions 21–30

21.
A triangular prism has a right-angled triangular cross-section with legs 5 cm and 12 cm, and prism length 20 cm. Find its volume.
22.
A cuboid has square base side $x$ cm and height 5 cm, SA 192 cm². Find $x$ .
23.
Rearrange $V = (1/3)\pi r^2 h$ , then find $h$ when $V = 100$ cm³, $r = 5$ .
24.
A solid metal sphere of radius 6 cm is melted and recast as a cylinder of radius 4 cm. Find the height.
25.
A cylinder open at the top has radius 3 cm and height 10 cm. Find the surface area (including base, no top).
26.
A cone has radius 6 cm and slant height 10 cm. Find the (a) curved surface area, (b) total SA.
27.
A cone has volume $48\pi$ cm³ and slant height 5 cm. Find the radius and height. (Hint: use Pythagoras for slant.)
28.
A composite shape: cylinder topped by a hemisphere. Cylinder r = 4, h = 10. Find total volume in terms of π.
29.
A cuboid has volume 360 cm³. Two sides are 6 and 5. Find the third.
30.
A swimming pool is a cuboid 25 m by 10 m by 2 m. Find (a) volume in m³, (b) capacity in litres.

PlatinumQuestions 31–40

31.
A cone has radius 6 cm and height 12 cm. The top is sliced off parallel to the base, producing a smaller cone of radius 3 cm. Find the volume of the remaining frustum (in terms of π).
32.
A spherical balloon has volume $36\pi$ cm³. (a) Find the radius. (b) The balloon's radius doubles. By what factor does the volume increase?
33.
Make $r$ the subject of $V = (4/3)\pi r^3$ .
34.
A skyscraper modelled as a cuboid is 154 m tall, 87 m wide, 30 m deep. (a) Find the glass area (4 vertical sides). (b) Find the space diagonal.
35.
A cylinder has radius $r$ and height $h$ where $h = 2r$ . Volume = $54\pi$ cm³. Find $r$ .
36.
A solid is formed by adding a cone to a cylinder. The cone and cylinder have the same radius 4 cm. The cylinder is 10 cm tall and the cone is 6 cm tall. Find the total volume.
37.
A hemispherical bowl has volume $\dfrac{2}{3}\pi r^3 = 250$ ml. Find $r$ (give 1 d.p.).
38.
Two cylinders are similar with linear scale factor 3. The smaller has volume 16 cm³. Find the larger volume.
39.
A pyramid has rectangular base 6 × 8 m and apex height 5 m above the centre of the base. Find the slant height to the midpoint of a long side.
40.
A cylinder of radius $r$ and height $h$ has surface area $A = 2\pi r^2 + 2\pi r h$ . Make $h$ the subject.