Surface Areas of Circle Shapes
# Surface Areas of Circle Shapes

GCSE(F), GCSE(H),

There are a number of formulae that need to be known for calculating circle-based shapes.

The surface area of the curved part of a **cone** is `A = pi xx text(base radius) xx text(slant length) = πrl`

The surface area of a **sphere** is `A = frac(4)(3) xx *π* xx text(radius)^2 = frac(4)(3)πr^2`

## Examples

1. A solid wooden cone has a base diameter of 24cm and a slant length of 40cm. What is the total surface area of the cone?

Answer: 1594.2 cm^{2}

Area of curved part = `πrl = π xx (24 ÷ 2) x 40 = 1507.2 text(cm)^2`

Area of base = `πr^2 = π xx (24 ÷ 2)^2 = 452.2text(cm)^2`

Total area = 1507.2 + 452.2 = 1959.4 cm^{2}

2. A globe has a diameter of 30 cm. What is the surface area of the globe?

Answer: 2826 cm^{2}

Area of a globe = `4πr^2`

`= 4 xx π xx (30 ÷ 2)^2`

= 2826 cm^{2}

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