volume and surface area of prisms, cylinders, and cones

Question

A farmer wants to buy a new water tank since he needs more water for his farm. His existing tank is a right circular cylinder which is 6 m high and 10 m wide. He was given two choices with the same cost.

1) The first one has twice the width of the original and half the height of the original.

2) The second one has twice the height of the original and half the width of the original.

Find the tank which accumulates a larger volume, and find the volume in cubic meters of that tank. (Use π = 3.14)

Answer 1

Volume of cylinder is πr²h

Volume of original: π(5)²(10)=785.4

Volume of tank 1: π(10)²(5)=1570.8

Volume of tank 2: π(2.5)²(20)=392.7

Area, determined by the width, is a square relationship to volume, while height is linear. Cutting the radius in half cuts the volume by a factor of 4. Doubling the height increases the volume of a factor of 2. Go with the bigger base and shorter top. ■