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Chapter 1: Problem 157

A cube has numerically equal volume and surface area calculate the volume of such a cube. (a) 2000 Unit (b) 216 Unit (c) 2160 Unit (d) 1000 Unit

Short Answer

Expert verified
The volume of the cube is 216 units.

Step by step solution

01

Write the formulas for volume and surface area of a cube

The volume (V) and surface area (A) of a cube are given by the following formulas, where s is the side length: Volume: \(V = s^3\) Surface Area: \(A = 6s^2\)
02

Set up the equation with numerically equal volume and surface area

Since the volume and surface area are numerically equal, we can write: \(s^3 = 6s^2\)
03

Solve the equation for side length s

Let's divide both sides of the equation by s^2: \(s = 6\)
04

Calculate the volume using the side length

Now that we have the side length, we can calculate the volume using the formula for the volume of a cube: \(V = s^3\) Substitute the value of s: \(V = 6^3\) \(V = 216\) units The volume of the cube is 216 units which corresponds to option (b).

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Most popular questions from this chapter

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