1540.72 – Waterbed Weight

Sammy wants to buy a waterbed but is worried about the strain on the floor of her room. The bed is 4 feet by 7 feet and is 8 inches deep. The casing for the water weighs 15 pounds, and the wooden frame for the bed weighs 95 pounds. A cubic foot of water weighs 62.4 pounds. What will the water bed weigh when it is filled?

Solution

V=4⋅7⋅23=563 cubic feetW=563⋅62.4+15+95=1274.8 lbs.\begin{aligned}V &= 4 \cdot 7 \cdot \dfrac{2}{3} \\&= \dfrac{56}{3} \text{ cubic feet} \\\\W &= \dfrac{56}{3} \cdot 62.4 + 15 + 95 \\[1em]&= 1274.8 \text{ lbs.}\end{aligned}

Before going ahead to get the waterbed, you could find figures for what the average adult weighs. Then figure out how many such people would weigh the same as the waterbed. Then you could imagine that many people in the room to see if it seems reasonable that the floor would hold the weight.

A small upright piano weighs between 300 and 400 pounds. A large one weighs between 600 and 800 pounds. A nine-foot concert grand piano weighs between 1000 and 1200 pounds.