Question

A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume? Drag and drop the labels to explain your answer.

Answer 1

Answer:

The rectangular prism has the greater volume

Step-by-step explanation:

Given

Prism:

$Length = Width = a$

$Height = h$

Cylinder

$Diameter = a$

$Height = h$

Required

Shape with greater volume

The volume of a rectangular prism is:

$Volume = Length * Base * Height$

So, we have:

$V_1 = a*a*h$

$V_1 = a^2h$

The volume of a cylinder is:

$Volume = \pi r^2h$

Where

$r = \frac{d}{2}$

$r = \frac{a}{2}$

So, we have:

$V_2 = \pi *(a/2)^2 h$

$V_2 = \pi *\frac{a^2}{4} h$

$\pi = 3.14$

So:

$V_2 = 3.14*\frac{a^2}{4} h$

$V_2 = \frac{3.14}{4} a^2h$

$V_2 = 0.785 a^2h$

So, we have:

$V_1 = a^2h$

$V_2 = 0.785 a^2h$

Both expressions have the same factor but different coefficient

The expression with greater coefficient has the greater volume

So, the $rectangular$ $prism$ has the $greater$ $volume$

Because: $1 > 0.785$