# Questions on surface area of cuboid

In this chapter we will try to solve questions related to total and lateral surface area of cuboid.

The formula for surface area is given below;

Total surface area of cuboid = 2 (lb + bh + hl)

Lateral surface area of cuboid = 2 (lh + bh)

Where, l, b & h are length, breadth and height of cuboid respectively.

## Surface area of cuboid – solved examples

Question 01
Consider the cuboid with length 40 cm, breadth 30 cm and height 50 cm. Find the lateral and total surface area of cuboid.

Solution
Lateral surface area = 2 (lh + bh)

Lateral surface area = 2 (40 x 50 + 30 x 50) = 7000 sq. cm

Hence, the lateral surface area is 7000 sq. cm.

Total surface area = 2 (lb + bh + hl)

Total surface area = 2 (40 x 30 + 30 x 50 + 50 x 40) = 9400 sq cm

Hence, the total surface area is 9400 sq. cm

Question 02
Chris purchased a gift for his brother and kept in a cuboid box of length 60 cm, breadth 40 cm and height 30 cm. How much area of colored paper required to gift wrap the whole box?

Solution
Calculating total area of the cuboid box.

Total area = 2 (lb + bh + hl)

Total area = 2 (60.40 + 40.30 + 30.60)

Total area = 2 (2400 + 1200 + 1800 ) = 10800 sq cm.

Hence, Chris need 10800 sq cm of gift paper to cover the whole box.

Question 03
Andy wants to white wash the walls of his room of length 3 m, width 5 meter and height 3 meter. If the cost of white washing is 10$per square meter, calculate the expense incurred by Andy. Solution Since, the painting has to be done on four walls of the room, we need to calculate the lateral surface area for cost calculation. Lateral Surface area = 2 (lh + bh) Lateral surface area = 2 (3 x 3 + 5 x 3) = 48 sq cm So, 48 sq meter of area is to be white washed. Now let’s calculate the cost. 1 sq meter ⟹ 10$

48 sq meter ⟹ 10 x 48 = 480 \$

Hence, the total cost will be 480 dollars.

Question 04
5 cubes are placed next to each other to form cuboid. calculate the ratio of surface area of cuboid to total surface area of 6 cubes

Solution
Let the length of cube be “a” units.

Surface area of one cube = \mathtt{6a^{2}}

Surface area of 5 cubes = \mathtt{5\times 6a^{2} =30a^{2}}

Now let’s calculate the total surface area of cuboid.

Length = 5a
Height = 5a

Total surface area of cuboid = 6 (lb + bh + hl)

Total surface area of cuboid = \mathtt{6\ \left( 5a^{2} +5a^{2} +25a^{2}\right) =210a^{2}}

Calculating the ratio of cuboid & all cubes;

\mathtt{\Longrightarrow \frac{210\ a^{2}}{30a^{2}}}\\\ \\ \mathtt{\Longrightarrow \ 7:1}

Hence 7 : 1 is the required ratio.

Question 05
The total and lateral surface area of cuboid is given as 400 sq m and 150 sq m. Calculate the area of base of cuboid

Solution
Total surface Area (4 walls + base & roof) = 400 sq m

Lateral surface area (4 walls) = 150 sq m.

Subtract both the area to get area of base and roof.
⟹ 400 – 150
⟹ 250 sq m

In cuboid, Area of base = Area of roof

Area of base = 250 / 2 = 125 sq m

Hence, area of base is 125 sq meter.