Question

How many square centimeters of construction paper does Reema need to exactly cover, with no overlap, \[5\] sides of a cube with edges that are \[12\] centimeters long?
A) \[60{\text{ c}}{{\text{m}}^2}\]
B) \[{\text{144 c}}{{\text{m}}^2}\]
C) \[300{\text{ c}}{{\text{m}}^2}\]
D) \[720{\text{ c}}{{\text{m}}^2}\]

Answer 1

Hint: Here we will use the formula for calculating the area of a cube as shown below:
\[{\text{Area}} = {\left( a \right)^2}\], where \[a\] is known as the side of the cube.

Complete step-by-step answer:
Step 1: We have given a cubic area whose sides are \[12\] centimeters long. By using the formula of area of the cube which states that:
\[{\text{Area}} = {\left( a \right)^2}\]
By substituting the value of the side of the cube which is \[12\] in the formula, we get:
\[ \Rightarrow {\text{Area}} = {\left( {12} \right)^2}\]
By opening the brackets and multiplying it into the RHS side of the expression \[{\text{Area}} = {\left( {12} \right)^2}\], we get:
\[ \Rightarrow {\text{Area}} = 144{\text{ c}}{{\text{m}}^2}\] (\[\because {\left( {12} \right)^2} = 144\])
Step 2: Now for calculating the area of the cube with \[5\] sides to cover it with the construction paper, we can simply multiply the number of sides with the area of the cube because the area
\[ \Rightarrow {\text{Area of cube with 5 faces}} = 5 \times \left( {{\text{Area of cube}}} \right)\]
By substituting the value of the area of the cube which is\[144{\text{ c}}{{\text{m}}^2}\] in the above expression, we get:
\[ \Rightarrow {\text{Area of cube with 5 faces}} = 5 \times \left( {144{\text{ c}}{{\text{m}}^2}} \right)\]
By doing the simple multiplication into the RHS side of the expression we get:
\[ \Rightarrow {\text{Area of cube with 5 faces}} = 720{\text{ c}}{{\text{m}}^2}\]
So, the construction paper required for covering the area of the cube with five faces is equals to \[720{\text{ c}}{{\text{m}}^2}\]
The construction paper required for covering the area of the cube with five faces is equal to \[720{\text{ c}}{{\text{m}}^2}\].

Option (D) is the correct answer.

Note: Students need to take care while using the formula for finding the area of the cube because the surface area of the cube equals the area of the six squares that covers it. The formula of the surface area is as shown below:
\[ \Rightarrow {\text{Surface area of cube}} = 6{a^2}\], where \[a\] is the side of the cube.
And the area of one of the single squares equals to \[{a^2}\].