# 018 Review Problem - Volume of Stone Bridge

**Problem 18**

A stone bridge has three equal semicircular arches resting on four equal rectangular piers. The radius of each arch is R, the dimensions of the piers L, W, H, while the distance from the top of each pier to the top of the bridge is D. If L = 50 ft., W = 5 ft., H = 10 ft., R = 6 ft., D = 12 ft., find the number of cubic yards of material used in building the bridge.

**Solution 18**

Volume

$V = A_bL$

$V = A_bL$

Where

$A_b = 22(56) - 3[ \, \frac{1}{2}\pi (6^2) \, ] - 3[ \, 12(10) \, ]$

$A_b = 702.354 ~ \text{ft.}^2$

Thus,

$V = 702.354(50)$

$V = 35,117.7 ~ \text{ft.}^3$

$V = 35,117.7 ~ \text{ft.}^3 \times \left( \dfrac{1 ~ \text{yd.}}{3 ~ \text{ft.}} \right)^3$

$V = 1300.7 ~ \text{yd.}^3$ *answer*

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