Edexcel IGCSE Math A 4.10.HA spheres cones and hemispheres

Practise advanced 3D mensuration by selecting the correct cone, sphere or hemisphere formula and combining parts of the solid carefully.

Exam points

Calculate volume or surface area for spheres, cones and hemispheres using the formulae.
Combine or subtract solid parts such as a cone joined to or cut by a hemisphere.
Use density or algebraic relationships after finding the required volume or surface area.

[Maximum number: 3]

Here are a solid sphere and a solid cylinder.

Figure for Question 4.10.HA The surface area and volume of a sphere and a right question 1 — Edexcel IGCSE Math A Higher

The radius of the sphere is $r \mathrm{~cm}$ .
The radius of the cylinder is $r \mathrm{~cm}$ .
The height of the cylinder is $2 r \mathrm{~cm}$ .
The total surface area of the cylinder is $k \pi \mathrm{~cm}^{2}$

Show that the ratio
total surface area of the cylinder: total surface area of the sphere is the same as the ratio
volume of the cylinder: volume of the sphere

$\text{Surface area ratio}=6r^2:4r^2=3:2$ $\text{Volume ratio}=2r^3:\frac{4}{3}r^3$ =6:4=3:2

Shown.

M1 for a correct surface-area ratio.
M1 for a correct volume ratio.
A1 oe, for example ratios could be $\frac{3}{2}:1$ .

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4.10.HA The surface area and volume of a sphere and a right question 1