Question

What is the volume of the cone?

Answer 1

Answer:

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

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

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

Best Buy: Sphere Clay

Step-by-step 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;

$Volume = \frac{1}{3}\pi r^2h$

From the attached diagram

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

Substitute these values in the above formula;

$Volume = \frac{1}{3} * 3.14 * 9^2 * 12$

$Volume = \frac{3052.08}{3}$

$Volume = 1017.36\ in^3$

Calculating Volume:Price Ratio

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 1017.36\ in^3$

$Total\ Cost = \ 12$ (Given)

$Volume:Price = \frac{1017.36\ in^3}{\ 12}$

$Volume:Price = 84.78 in^3/$

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

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;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

$Total\ Cost = \ 30$ (Given)

$Volume:Price = \frac{3052.08\ in^3}{\ 30}$

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

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

SPHERE

Calculating Volume

The volume of a sphereis calculated as thus;

$Volume = \frac{4}{3}\pi r^3$

From the attached diagram

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

Substitute these values in the above formula;

$Volume = \frac{4}{3} * 3.14 * 9^3$

$Volume = \frac{9156.24}{3}$

$Volume = 3052.08\ in^3$

Calculating Volume-Price ratio

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

$Total\ Cost = \ 28$ (Given)

$Volume:Price = \frac{3052.08\ in^3}{\ 28}$

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

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

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