Question

What is the volume of the cone?

What is the volume of the cylinder?

What is the volume of the sphere?

At the craft store discussed above, the clay cone is $12, the clay cylinder is $30, and the clay sphere is $28. Which is the best buy? Explain.

Hint: Which shapes gives you more clay for less money?

Answer 1

`Volume = 1017.36\ in^3` -- Cone

`Volume = 3052.08\ in^3` -- Cylinder

`Volume = 3052.08\ in^3` -- Sphere

Best Buy: Sphere Clay

Explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

CONE

Calculating Volume

The volume of a cone is calculated as thus;

`Volume = (1)/(3)\pi r^2h`

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and
`\pi = 3.14`

Substitute these values in the above formula;

`Volume = (1)/(3) * 3.14 * 9^2 * 12`

`Volume = (3052.08)/(3)`

`Volume = 1017.36\ in^3`

Calculating Volume:Price Ratio

The unit cost of the cone is calculated as thus;

`Volume:Price = (Volume)/(Total\ Cost)`

Where

`Volume = 1017.36\ in^3`

`Total\ Cost = \$12` (Given)

`Volume:Price = (1017.36\ in^3)/(\$ 12)`

`Volume:Price = 84.78 in^3/\$`

`Volume:Price = 84.78 in^3:\$1`

CYLINDER

Calculating Volume

The volume of a cylinder is calculated as thus;

`Volume = \pi r^2h`

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and
`\pi = 3.14`

Substitute these values in the above formula;

`Volume = 3.14 * 9^2 * 12`

`Volume = 3052.08\ in^3`

Calculating Volume:Price Ratio

The unit cost of the cone is calculated as thus;

`Volume:Price = (Volume)/(Total\ Cost)`

Where

`Volume = 3052.08\ in^3`

`Total\ Cost = \$30` (Given)

`Volume:Price = (3052.08\ in^3)/(\$ 30)`

`Volume:Price = 101.736\ in^3/\$`

`Volume:Price = 101.736\ in^3:\$1`

SPHERE

Calculating Volume

The volume of a sphereis calculated as thus;

`Volume = (4)/(3)\pi r^3`

From the attached diagram

Radius, r = 9 inches; and
`\pi = 3.14`

Substitute these values in the above formula;

`Volume = (4)/(3) * 3.14 * 9^3`

`Volume = (9156.24)/(3)`

`Volume = 3052.08\ in^3`

Calculating Volume-Price ratio

The unit cost of the cone is calculated as thus;

`Volume:Price = (Volume)/(Total\ Cost)`

Where

`Volume = 3052.08\ in^3`

`Total\ Cost = \$28` (Given)

`Volume:Price = (3052.08\ in^3)/(\$ 28)`

`Volume:Price = 109.003\ in^3/\$`

`Volume:Price = 109.003\ in^3:\$1`

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay