Find the Square Base Side Length of a Cuboid with Volume 640 cm³ and Height 10

Given the following cuboid such that its base is a square.

The height of the cuboid is equal to 10 The volume of the cuboid is equal to 640 cm³.

Find the length of the side of the base

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the base edge of the box
00:04 The base of the box is a square according to the given data, therefore the edges are equal
00:11 We will use the formula for calculating box volume
00:14 Height multiplied by length multiplied by width
00:18 We will substitute appropriate values and solve to find A
00:22 Let's isolate A
00:28 When taking the square root, there are 2 solutions: negative and positive
00:31 The negative solution is not relevant, it must be a physical size
00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following cuboid such that its base is a square.

The height of the cuboid is equal to 10 The volume of the cuboid is equal to 640 cm³.

Find the length of the side of the base

2

Step-by-step solution

To find the length of the side of the square base, we'll apply the formula for the volume of a cuboid:

V=l2×h V = l^2 \times h

Step 1: Substitute the given values into the equation.

We have:

640=l2×10 640 = l^2 \times 10

Step 2: Simplify the equation.

Divide both sides by 10:

64=l2 64 = l^2

Step 3: Solve for l l .

Take the square root of both sides:

l=64 l = \sqrt{64}

l=8 l = 8

Thus, the length of the side of the base of the cuboid is 8 8 cm.

3

Final Answer

8 8

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

121212888555

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