Question

1. the cube and the rectangular prism below have the same volume. find the height of the rectangular prism to the nearest tenth.

cylinder: a 3 - d object that has circles as the bases.
volume of a cylinder:

find the volume for each cylinder to the nearest tenth.
1)
2)
3)

find the volume of each cylinder in terms of π.
4)
5)

Explanation:

Step1: Calculate the volume of the cube

The volume formula for a cube is \(V = s^3\), where \(s = 8\) cm.

$$V_{cube}=8^3=512\space cm^3$$

Step2: Set up the volume formula for the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 14\) cm, \(w = 6\) cm, and \(V = 512\space cm^3\). We need to find \(h\).

$$512=14\times6\times h$$

$$512 = 84h$$

Step3: Solve for \(h\)

$$h=\frac{512}{84}\approx6.1\space cm$$

Answer:

The height of the rectangular prism is approximately \(6.1\) cm.