Grade 7

Volume and surface area practice

A prism or cylinder has volume base × height; a pyramid or cone has one third of that. Surface area is the total area of the net.

Basic, Standard, Advanced: Grade 7 · Term 3

BasicStandardAdvancedMix

0Make a worksheet on this topic

Volumes

Volume (base area

S

, height

h

)

\text{prism, cylinder: } V = Sh,\qquad \text{pyramid, cone: } V = \frac{1}{3}Sh

Example: a cone with radius $3$ cm and height $4$ cm has volume $\frac{1}{3} \times \pi \times 3^2 \times 4 = 12\pi$ cm $^3$ .

Surface area and cone nets

The curved surface of a cylinder unrolls to a rectangle: height × circumference. The curved surface of a cone unrolls to a sector with radius equal to the slant height $\ell$ and arc equal to the base circumference.

\text{central angle} = 360^\circ \times \frac{r}{\ell},\qquad \text{curved area} = \pi \ell r

Spheres and solids of revolution

Sphere (radius

r

)

V = \frac{4}{3}\pi r^3,\qquad S = 4\pi r^2

Rotating a rectangle about one side gives a cylinder; rotating a right triangle about a leg gives a cone. A sphere that fits exactly in a cylinder has $\frac{2}{3}$ of the cylinder's volume.

Q1BasicGr 7 · Term 3Solid figures

Find the volume of a cylinder with base radius 6 cm and height 8 cm.

Answer

288\pi\text{ cm}^3

Solution

Base area × height
$\pi \times 6^2 \times 8 = 288\pi\ (\text{cm}^3)$

Q2StandardGr 7 · Term 3Solid figures

Find the surface area of a cylinder with base radius 6 cm and height 4 cm.

Answer

120\pi\text{ cm}^2

Solution

Two bases
$\pi \times 6^2 \times 2 = 72\pi$
Curved surface (height × circumference)
$4 \times 2\pi \times 6 = 48\pi$
Total
$72\pi + 48\pi = 120\pi\ (\text{cm}^2)$

Q3AdvancedGr 7 · Term 3Solid figures

Find the volume and the surface area of a sphere with radius 2 cm.

Answer

volume $\frac{32}{3}\pi\text{ cm}^3$
surface area $16\pi\text{ cm}^2$

Solution

Volume
$\frac{4}{3}\pi \times 2^3 = \frac{32}{3}\pi\ (\text{cm}^3)$
Surface area
$4\pi \times 2^2 = 16\pi\ (\text{cm}^2)$

Q1BasicGr 7 · Term 3Solid figures

Find the volume of a cone with base radius 4 cm and height 3 cm.

Q2StandardGr 7 · Term 3Solid figures

A triangular prism has a right-triangle base with sides 6 cm, 8 cm and 10 cm, and height 9 cm. Find its surface area.

Q3AdvancedGr 7 · Term 3Solid figures

Find the volume of the solid formed by rotating the rectangle once about line ℓ.

Teleport

Main features

On this page

Topics

Display

Volume and surface area practice

Volumes

Surface area and cone nets

Spheres and solids of revolution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Math problem generator

Volumes

Surface area and cone nets

Spheres and solids of revolution

Worked examples

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Practice problems

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Related topics

Plane figures