Calculate Cuboid Volume: 12cm Base Perimeter, 8cm Height Problem

Given an cuboid with a square base

Given that the perimeter of the base is 12 cm

Its height is equal to 8 cm

Is it possible to calculate the volume of the cuboid?

Video Solution

Solution Steps

00:00 Calculate the volume of the box if possible

00:03 Square base according to the data, therefore equal sides

00:10 The perimeter of the square equals the sum of its sides

00:14 Let's substitute appropriate values and solve for side A

00:17 This is side A

00:22 Let's draw the box

00:29 Let's use the formula for calculating box volume

00:33 Height times length times width

00:38 Let's substitute appropriate values and solve for the volume

00:43 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Let's work through each step:

Step 1: The perimeter of the square base is given as 12 cm. We can find the side length $s$ of the square using the perimeter formula:

$P = 4s$

So,

$12 = 4s$ which implies $s = \frac{12}{4} = 3 \text{ cm}$ .

Step 2: The area of the square base is then:

$\text{Area} = s^2 = 3^2 = 9 \text{ cm}^2$ .

Step 3: To find the volume of the cuboid, we use the formula for volume:

$V = \text{Base Area} \times \text{Height} = 9 \times 8 = 72 \text{ cm}^3$ .

Thus, we have successfully determined that it is possible to calculate the volume of the cuboid, and the volume is $72 \text{ cm}^3$ .

Therefore, the correct answer to the problem is Yes.