Question

An artist needs to design a six-foot tall platform to hold a statue for a park. In order to be stable, each base of the platform must cover approximately 20 square feet. Which of these shapes will use the least amount of stone for the base of the platform?

Answer 1

The cylinder you have to find the volume of each shape

Answer 2

Answer: Cylinder

Explanation:

Since, that shape which has the least volume will be use least amount of stone,

Here, The first figure is a Cuboid having length 6 feet, width 4 feet and height 6 feet,

Thus, the volume of first figure = 6 × 4 × 6 = 144 cube feet,

Second figure is a cylinder having diameter 5 feet and height 6 feet,

Thus, the volume of second figure =
`\pi ((5)/(2))^2* 6`

= 3.14 × 2.5 × 2.5 × 6

= 117.75 cube feet ( Approx )

Third figure is a triangular prism having the equilateral base of side 8 feet and has height 6 feet,

Thus, the volume of the third figure = √3/4 × 64× 6 = 96√3 = 166.276878 ≈ 166.28 cube feet.

Now, Fourth figure is a cuboid having length = 5 feet, width = 5 feet and height = 6 feet,

Thus, the volume of this cuboid = 5 × 5 × 6 = 150 cube feet,

Therefore, by the above explanation it is clear that the volume of cylinder is least,

⇒ Cylinder shaped statue will use the least amount of stone for the base of the platform.