# Lamp cone

Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.

Correct result:

S =  1797 cm2

#### Solution:

$r_{1}=12/2=6 \ \text{cm} \ \\ r_{2}=32/2=16 \ \text{cm} \ \\ h=24 \ \text{cm} \ \\ s=\sqrt{ h^2+(r_{2}-r_{1})^2 }=\sqrt{ 24^2+(16-6)^2 }=26 \ \text{cm} \ \\ S=\pi \cdot \ (r_{1}+r_{2}) \cdot \ s=3.1416 \cdot \ (6+16) \cdot \ 26=1797 \ \text{cm}^2$

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