Geometry question

Question

two rectangular prism's have equal heights but unequal bases. Each dimension of the smaller solids base is half each dimension of the larger solids base. The volume of the larger solid is how many times as great as the volume of the smaller solid?

Answer 1

Consider that the volume of a rectangular prism is L X W X H (length times width times height).

 

Let's call the volume of the smaller solid = V₁. Then, V₁ = L₁ * W₁ * H₁

 

Let's now call the volume of the larger solid V_2. Then V₂ = L₂ * W₂ * H₂

 

We know from the problem that H₁ = H₂

 

We also know that L₁ = 1/2 L₂, and W_{1 =} 1/2 W₂

 

Therefore, we can express V₁ as 1/2 L₂ * 1/2 W₂ * H₂ = 1/4  * L₂ * W₂ * H₂

 

You should now be able to determine how much greater the volume of the larger solid is compared to the smaller solid.

Answer 2

Volume = L (length) X W (width) x H (height)

V_smaller = L/2*W/2*H

V_larger = L*W*H

 

Compute V_larger / V_smaller for your answer (which is 4)