The surface area of the solid is made up of the curved surface area of the cylinder, half of the surface area of the sphere and the area of the circular base.
Find each area individually and add them together.

Find the curved surface area (CSA) of the cylinder
If the cylinder was unrolled its curved surface area would be a rectangle with a length equal to the circumference of the circular base and a width equal to the height of the cylinder.

$\begin{array}{rcl} CSA & = & 2 π r^{} \times h \\ = & (2) (7) π \times 12 \\ = & 168 π \end{array}$

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Find the surface area (SA_HS) of half of the sphere.

$\begin{array}{rcl} {SA}_{HS} & = & \frac{1}{2} (4 π r^{2}) \\ = & \frac{1}{2} (4 π {(7)}^{2}) \\ = & \frac{1}{2} (196 π) \\ = & 98 π \end{array}$

[1]

Find the area (A_c) of the circular base.

$\begin{array}{rcl} A_{C} & = & π r^{2} \\ = & {(7)}^{2} π \\ = & 49 π \end{array}$

[1]

Add these together to find the total surface area (TSA) of the solid

$\begin{array}{rcl} TSA & = & CSA + {SA}_{HS} + A_{C} \\ = & 168 π + 98 π + 49 π \\ = & 315 π {cm}^{2} \end{array}$

Either leave your answer as an exact value or convert to a decimal and round to 3 s.f.

990 cm² [1]
Answers in the range 989.58 to 989.73 are also accepted if you have not rounded to 3 s.f.

Volume & Surface Area (CIE IGCSE Maths: Extended)

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