# 004 Hemispherical dome covered with gold

**Example 004**

The surface of a hemispherical dome whose diameter is 10 m is to be covered with gold leaf which costs \$0.25 per square centimeter. What must be paid for the gold leaf?

**Solution 004**

Surface area of the dome

$A = \frac{1}{2}\pi d^2 = \frac{1}{2}\pi (10^2)$

$A = \frac{1}{2}\pi d^2 = \frac{1}{2}\pi (10^2)$

$A = 50\pi \, \text{ m}^2 = 50\pi \, \text{ m}^2 \left( \dfrac{100 \, \text{ cm}}{1 \, \text{ m}} \right)^2$

$A = 500\,000\pi \, \text{ cm}^2$

Amount to be paid for gold leaf

$C = 500\,000\pi (0.25)$

$C = \$392\,699.08$ *answer*

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