Question

37. A company is choosing between two tanks for mixing chemicals Bothhave the same price, so the company plans to choose the one thatcan holdtanksthemost chemicals. The first tank conical with a diameter of 10 feet anda heightof 15 feet. The second tank is a hemisphere with a radius of 5.5 feetOne cubic foot 7.48 gallons

Answer 1

Given:
1st tank: conical with diameter of 10 feet and height of 15 feet.
2nd tank: hemisphere with a radius of 5.5 feet

volume of a cone = πr² h/3
V = 3.14 * (5ft)² * 15ft/3
V = 3.14 * 25ft² * 5ft
V = 392.5 ft³

392.5 ft³ * 7.48 gallons/ft³ = 2,935.9 gallons

volume of a hemisphere = (2πr³)/3
V = [2 * 3.14 * (5.5ft)³]/3
V = (2 * 3.14 * 166.375 ft³)/3
V = 1,044.835 ft³/3
V = 348.28 ft³

348.28 ft³ * 7.48 gallons/ft³ = 2,605.13 gallons

Answer 2

Volume of the conical tank = 1/3pi*r^2 * h = 1/3pi * (10/2)^2 * 15 = 125pi cubic feet or 392.7 cubic feet = 392.7 * 7.48 gallons = 2937 gallons.

Volume of the hemispherical tank = 2/3pi * r^3 = 2/3pi * (5.5)^3 = 348.5 cubic feet = 348.5 * 7.8 gallons = 2606 gallons

Hence the conical tank will contain more chemicals