# How do you find the area of the top and lateral surface of a cylindrical water tank with radius 20 ft and height 30 ft.?

Nov 12, 2016

Exact value $\to 1600 \pi f {t}^{2}$
Approx value$\to 5026.5 f {t}^{2}$

#### Explanation:

Interesting that the bottom is not required in the solution.

Assumption: The top is not curved but flat.

Let the unit of measurement be $f t$ for feet

Area of top $\to \pi {r}^{2} \to \pi \times {\left(20 f t\right)}^{2} \approx 1256.6 f {t}^{2}$

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Lateral area $\to$ height x circumference $\to 30 f t \times \pi D f t$

$= 30 f t \times \pi 40 f t \approx 3769.9 f {t}^{2}$
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It is more precise to calculate the sum in this way:

$\left[\pi {20}^{2}\right] f {t}^{2} + \left[30 \times 40 \pi\right] f {t}^{2}$

$\pi \left({20}^{2} + 1200\right) f {t}^{2}$

$1600 \pi f {t}^{2} \approx 5026.5 f {t}^{2}$