Question

A homeowner's deck can support a maximum weight of 2,000 pounds. They fill their "circular hot tub" measuring 6ft in diameter to a depth of 2.5 ft with water (density=1.00g/mL). Will their deck collapse? Given V=pir²h.

a. Yes, the deck will collapse.
b. No, the deck will not collapse.

Answer 1

By calculating the volume and weight of the water in the hot tub and comparing it to the deck's maximum support capacity, we find that the deck will likely collapse since the weight of the water (approximately 4415.57 pounds) exceeds the maximum weight support limit of 2000 pounds.

Step-by-step explanation:

To determine if the homeowner's hot tub will cause their deck to collapse, we need to calculate the weight of the water in the hot tub and compare it to the maximum weight support of the deck. The volume (V) of water in a circular hot tub can be calculated using the formula V = πr²h, where π is approximately 3.14159, r is the radius of the hot tub, and h is the depth of water. Since the diameter of the hot tub is 6 feet, the radius (r) is 3 feet. The depth (h) is given as 2.5 feet.

Using these values, we find the volume of the water to be V = π(3²)(2.5), which equals approximately 70.69 cubic feet. Since the density of water is 1.00 g/mL, or equivalently 62.43 lbs/ft³, the weight of the water is then 70.69 ft³ × 62.43 lbs/ft³, which is approximately 4415.57 pounds. Since this weight exceeds the deck's maximum support weight of 2000 pounds, the deck will likely collapse under the weight of the filled hot tub.