Question

a box containing food is described below.

• the bottom part of the box is shaped like a square prism with a height of 5 centimeters.
• the top part of the box is shaped like a square pyramid with a height of 3 centimeters.
• the volume of the top part of the box is 100 cubic centimeters.

what is the volume of the bottom part of the box?
4 of 4 questio
125 cm³
100 cm³
800 cm³
500 cm³

Explanation:

Step1: Find the base area of the square pyramid

The volume formula for a square pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the base area and \(h\) is the height. Given \(V = 100\space cm^{3}\) and \(h=3\space cm\).
We can solve for \(B\) using the formula \(B=\frac{3V}{h}\).
Substitute \(V = 100\) and \(h = 3\) into the formula: \(B=\frac{3\times100}{3}=100\space cm^{2}\).

Step2: Calculate the volume of the square prism

The volume formula for a square prism (cuboid with square base) is \(V=Bh\), where \(B\) is the base area and \(h\) is the height.
We found \(B = 100\space cm^{2}\) from the pyramid part, and the height of the prism \(h = 5\space cm\).
Substitute \(B = 100\) and \(h = 5\) into the formula: \(V=100\times5 = 500\space cm^{3}\).

Answer:

\(500\space cm^{3}\) (the fourth option)