Part 4: Installation of Hot Tub Your client has requested the installation of a hot tub on the deck behind their house. The hot tub is a cylinder, 8 feet in diameter and 32 inches deep. The tub weighs 925 pounds (empty). The deck on which the tub will be placed can support a maximum of 11,500 pounds. You are not certain that the deck will support the hot tub. a) Determine the volume of the water of the hot tub in cubic feet. Round to the nearest whole number. 5) Determine the capacity of the hot tub, in gallons. Round to the nearest whole number. (1 cubic foot=7.48 gallons) How much will the hot tub weigh when it is filled with water (1 gallon=8.35 lbs)? Round to the nearest whole number. If your client has 6 friends in their hot tub who together weigh 1150 pounds, will the deck support this hot tub, or will you ask come crashing through the deck?

9514 1404 393

  4) 134ft³

  5) 1002 gallons; 9292 lb filled

  6) the deck will support

Step-by-step explanation:

4) The volume of a cylinder is given by the formula ...

  V = πr²h = (π/4)d²h

The volume of this hot tub is ...

  V = (π/4)(8 ft)²(32/12 ft) = 128π/3 ft³ ≈ 134 ft³

__

5) The volume in gallons is ...

  (134 ft³)×(7.48 gal/ft³) ≈ 1002 gal

The weight of the water in the tub will be ...

  (1002 gal)(8.35 lb/gal) = 8367 lb

So, the weight of the tub filled with water is ...

  925 lb +8367 lb = 9292 lb

__

6) Then the total weight of tub, water, and friends is ...

  9292 lb + 1150 lb = 10,442 lb < 11,500 lb

The deck will support this hot tub.

__

Additional comment

In the above calculations, we have used the rounded values at each stage of the calculation. This results in a calculated weight that is perhaps 5 lbs less than the weight calculated without rounding intermediate values.

The capacity of the deck is about 10% more than the weight of the hot tub and friends. Ordinarily, a substantially greater margin would be preferred. Here, the deck is at risk of failure if 6 more friends show up than are expected.

b

step-by-step explanation: