A solid rectangular box has a length of 6 centimeters, a width of 4 centimeters, and a hei… — GRE General Test

A solid rectangular box has a length of $6$ centimeters, a width of $4$ centimeters, and a height of $5$ centimeters. What is the total surface area, in square centimeters, of the box?

A
$74$
B
$120$
$148$ Answer
D
$240$
E
$288$

Answer

The total surface area of the rectangular box is

148

square centimeters.

The total surface area of a rectangular solid with length

l

, width

w

, and height

h

is given by

2(lw + lh + wh)

. Substituting

l = 6

w = 4

, and

h = 5

yields

2(6 \cdot 4 + 6 \cdot 5 + 4 \cdot 5) = 2(24 + 30 + 20) = 2(74) = 148

square centimeters.

Step-by-Step Solution

Identify the given dimensions of the rectangular box.

Length

l = 6

cm, width

w = 4

cm, and height

h = 5

cm.

These dimensions are required to compute the area of each face.

Calculate the surface area of the three distinct face pairs.

Top and bottom faces:

6 \times 4 = 24

; Front and back faces:

6 \times 5 = 30

; Left and right side faces:

4 \times 5 = 20

A rectangular solid has six rectangular faces grouped into three identical pairs.

Apply the surface area formula

A = 2(lw + lh + wh)

A = 2(24 + 30 + 20) = 2(74) = 148

square centimeters.

Summing the area of all six faces gives the total surface area.

Key Concept

Surface Area of a Rectangular Solid

Question

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Step-by-Step Solution

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