Examples with solutions for Surface Area of a Cuboid: Calculate The Missing Side based on the formula

Exercise #1

Look at the cuboid of the figure.

Its surface area is 122 cm².

What is the width of the cuboid?

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Video Solution

Step-by-Step Solution

To solve the problem, let's recall the formula for calculating the surface area of a box:

(width*length + height*width + height*length) *2

Let's substitute the known values into the formula, and we'll denote the missing side as X:

2*(3*7+7*X+3*X) = 122

2*(21+7x+3x) = 122

2(21+10x) = 122

Let's expand the parentheses:

42+20x=122

Let's move terms:

20x=122-42

20x=80

Let's simplify:

x=4

And that's the solution!

Answer

4 cm

Exercise #2

The surface area of a cube is 24 cm². How long is the cube's side?

Video Solution

Answer

2 2

Exercise #3

Given the cuboid of the figure:

Given that the marked face is a square whose sides are 7 cm

Find the length of the cuboid, given that its surface area is 406 cm².

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Video Solution

Answer

11 cm

Exercise #4

Look at the cuboid in the figure below.

Its surface area 752 cm².

Calculate X.

121212888X+4X+4X+4

Video Solution

Answer

10 cm

Exercise #5

Look at the cuboid of the figure below.

Its surface area is 124 cm².

Calculate the length of the cuboid.

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Video Solution

Answer

9 9 cm

Exercise #6

The area of the cube is 486.

Calculate the length of the side of the cube and its volume.

S=486S=486S=486aaa

Video Solution

Answer

a=9,V=729 a=9,V=729

Exercise #7

The surface area of a cube is 24 cm².

How long are the sides of the cube?

Video Solution

Answer

2

Exercise #8

A cuboid has the following dimensions:

4×3x×2y 4\times3x\times2y

Its surface area is:

66x+56 66x+56

What is the value of y y ?

Video Solution

Answer

3.5 3.5 cm

Exercise #9

Below is an unfolded cuboid.

The surface of the cuboid is 172 cm².

Calculate X.

222777XXX

Video Solution

Answer

8 cm

Exercise #10

The surface area of the rectangular prism in the diagram is 4x2+24x 4x^2+24x .

Calculate the height of the rectangular prism.

XXX2X2X2X

Video Solution

Answer

4 4 cm