Total surface area of cuboid - Example

 Given below is a cuboid having its dimension given as length = 8 cm, width = 6 cm and height = 5 cm, find the TSA of a cuboid.

Solution

Given:

h = 5 cm

w = 6 cm

l = 8 cm

Using the formula: TSA = 2 (lw + wh + hl)

2( (8×6) + (6×5) + (5×8))

= 2(48 + 30 + 40)

= 2(118)

= 236

So, the total surface area of this cuboid is 236 cm².

Example 2:

The dimensions of a cuboid are given as follows:

Length = 4.8 cm

Width = 3.4 cm

Height = 7.2 cm.

Find the Total Surface area and the Lateral Surface area.

Solution:

The total surface area is given as

TSA = 2 (lw + wh + hl)

=2((4.8 ×3.4) + (3.4×7.2) + (7.2×4.8))

= 2(16.32 +24.48 +34.56)

= 2(75.36) cm²

Therefore, TSA of a cuboid= 150.72 cm

Also, the lateral surface area = 2 h (l + w)

= 2×7.2 (4.8 + 3.4)

= 14.4 (8.2) = 118.08

Therefore, LSA of a cuboid = 118.08 cm²

Question 1. If six cubes of 10 cm edge are joined end to end, then the surface area (in sq. cm) of the resulting solid is

1. 3600
2. 3000
3. 2600
4. 2400

Answer: C. If six cubes are joined together, then the resulting solid is a cuboid. The dimensions of the solid are as follows,

length =60cm, breadth = 10 cm and height = 10 cm. Now, the total surface area of a cuboid is given by

2 [( l × b ) + ( b× h ) + ( l× h )]

By substituting the values, we get,
= 2 [( 60× 10 ) + ( 10× 10 ) + ( 60× 10)] = 2 ( 1300) = 2600 cm²

Question 2. John built a rectangular cardboard box 25 cm high with a square base and a volume of 2500 cm³. Then he realized he did not need a box that large, so he chopped off the height of the box reducing its volume to 1,000 cm³. Was the new box cubical? Also, state its’ height.

1. 20 cm
2. 10 cm
3. 30 cm
4. 40 cm

Answer: B. Volume of cuboid (V)  = length × breadth × height = Base area × height.

Given, V = 2500 cm3, height = 25 cm. By substituting the values in the formula, we get

Base area = 2500/25 = 100 cm²
Given that the base is a square. This means that the length = breadth. Therefore, the length of square base =  √100 = 10 cm
After chopping, new volume = 1000 = 10 ×10 x new height
Therefore, new height = 1000/ 10 × 10 = 10 cm
As all the dimensions of the solid, l, b, h measure the same, the resulting solid is a cube.

Answer The Following

Question 3: Find the surface area of a cube whose edge is 5 cm?

Answer: Cube is a type of cuboid in which the length, breadth and height measure the same. The formula to calculate the total surface area of a cuboid is 2 [( l × b ) + ( l× h ) + ( b× h )]. As l=b=h=a, the total surface area of cube= 2 [( a × a ) + ( a× a ) + ( a× a )] = 2 [3a2] = 6a2. To sum up,

Total surface area of cube = 6a2

Given that a = 5 cm. Thus,

T.S.A =6(52) = 6 X 25 = 150 cm2

Question 4: Define volume.

Answer: Volume is the amount of space that is occupied by a three-dimensional solid object. The unit of measurement of volume is the cubic meter.

Question 5: What is the lateral surface area of a cube of edge 10cm?

Answer: We know that the lateral surface area of a cuboid is given by 2(l+b)h. As a cube is a cuboid in which l=b=h=a, lateral surface area of cube = 2(a+a)a = 4a2. In simple terms

Lateral surface area of cube = 4a2

Given that a = 10 cm. Thus,

LSA = 4(102) = 400 cm2

Question 6: How do you measure the volume of water?

Answer: Basically, we can’t measure the volume of water until it is stored in a container, which can be a cube, cuboid, cylinder, cone, etc. And once it is inside a container we have to calculate the volume of the container to know the volume of water.