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

Breadth = a

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.**