GCSE Maths | Volume & Surface Area
- volume of prism = area of cross-section x length
Question 1
Question 2
Question 3
Question 4
Work out the height of the cylinder
a. The volume of a cylinder is 100π cm³ and the radius is 5 cm.
b. The volume of a cylinder is 75π m³ and the radius is 3 m.
c. The volume of a cylinder is 144π cm³ and the radius is 6 cm.
d. The volume of a cylinder is 200π m³ and the radius is 5 m.
e. The volume of a cylinder is 48π cm³ and the radius is 4 cm.
f. The volume of a cylinder is 314 cm³ and the radius is 5 cm.
g. The volume of a cylinder is 452 m³ and the radius is 6 m.
h. The volume of a cylinder is 1256 cm³ and the radius is 10 cm.
i. The volume of a cylinder is 283 m³ and the radius is 3 m.
j. The volume of a cylinder is 942 cm³ and the radius is 5 cm.
Question 5
Work out the radius of the cylinder
a. The volume of a cylinder is 100π cm³ and the height is 5 cm.
b. The volume of a cylinder is 75π m³ and the height is 3 m.
c. The volume of a cylinder is 144π cm³ and the height is 6 cm.
d. The volume of a cylinder is 200π m³ and the height is 5 m.
e. The volume of a cylinder is 48π cm³ and the height is 4 cm.
f. The volume of a cylinder is 314 cm³ and the height is 5 cm.
g. The volume of a cylinder is 452 m³ and the height is 6 m.
h. The volume of a cylinder is 1256 cm³ and the height is 10 cm.
i. The volume of a cylinder is 283 m³ and the height is 3 m.
j. The volume of a cylinder is 942 cm³ and the height is 5 cm.
- Volume of a sphere: V = (4/3) x π x r3
Question 6
Work out the volume of the sphere
Question 7
Work out the radius of the sphere
a. The volume of a sphere is 36π cm³.
b. The volume of a sphere is 288π cm³.
c. The volume of a sphere is ⁴⁄₃π m³.
d. The volume of a sphere is 500π/3 cm³.
e. The volume of a sphere is 2304π cm³.
f. The volume of a sphere is 113.04 cm³.
g. The volume of a sphere is 904.32 cm³.
h. The volume of a sphere is 4.19 m³.
i. The volume of a sphere is 2144.66 cm³.
j. The volume of a sphere is 179.59 cm³.
- Surface area of a sphere: S = 4 x π x r2
Question 8
Work out the surface area of the sphere
Question 9
Work out the radius of the sphere
a. Surface area = 16π cm²
b. Surface area = 100π cm²
c. Surface area = 324π m²
d. Surface area = 484π cm²
e. Surface area = 64π m²
f. Surface area = 113.04 cm²
g. Surface area = 452.16 cm²
h. Surface area = 1256 m²
i. Surface area = 615.44 cm²
j. Surface area = 2463.01 m²
- Volume of cone = 1/3 x volume of cylinder
- Volume of cone = 1/3 x π x r2 x h
Question 10
Work out the volume of the cone
Question 11
Work out the height of the cone
a. Volume = 12π cm³, radius = 3 cm
b. Volume = 50π cm³, radius = 5 cm
c. Volume = 108π m³, radius = 6 m
d. Volume = 147π cm³, radius = 7 cm
e. Volume = 150 cm³, radius = 5 cm
f. Volume = 452 cm³, radius = 6 cm
g. Volume = 1017 m³, radius = 9 m
h. Volume = 308 cm³, radius = 7 cm
Question 12
Work out the radius of the cone
a. Volume = 16π cm³, height = 12 cm
b. Volume = 100π cm³, height = 12 cm
c. Volume = 54π m³, height = 18 m
d. Volume = 196π cm³, height = 12 cm
e. Volume = 150 cm³, height = 18 cm
f. Volume = 113 cm³, height = 12 cm
g. Volume = 1017 m³, height = 27 m
h. Volume = 308 cm³, height = 12 cm
- Curved surface area of cone = πrl
- Surface area of cone = πrl + πr2
Question 13
Work out the surface area of the cone
Question 14
Work out the surface area of the cone
Question 15
Work out the length of the cone
Question 16
Work out the radius of the cone
Question 17
Work out the height of the cone
- volume of cone = 1/3 x π x r2 x h
- volume of frustum = volume of big cone - volume of small cone
- the small cone and big cone are similar shapes
- the length scale factor applies to both the height of cones and the radius of the cones
Question 18
Work out the volume of the frustum
Question 19
Work out the volume of the frustum
Question 20
Question 21
Work out the volume of the frustum
