Question

Find the lateral surface area and the total surface area of a cuboid which is 8m long, 5m broad, and 3.5m high.

Answer 1

Hint: Here, first let us draw the figure of a cuboid indicating the given measurements then, use the formula for lateral surface area of a cuboid = $ 2h\left( l+w \right) $ and then find the total surface area of a cuboid by using, Total surface area = $ 2\left( lb+bh+lh \right) $ .

Complete step-by-step answer:
Let us first draw the figure with the given measurements and indicate them on the diagram of cuboid.

Here, we have a cuboid of about 8m in length, 5m in breadth and 3.5m in height.
Therefore, $ l=8\,m $ , $ b=5\,m $ , $ h=3.5\,m $ .
Now, let us find (i) the lateral surface area of the cuboid (ii) total surface area of the cuboid
We know,
Lateral surface area of a cuboid = $ 2h\left( l+w \right) $ , where \[w\]= width is also known as breadth.
Let us substitute the given values in the formula and find the value of the lateral surface of a cuboid, we get
Lateral surface area = 2 (3.5) $ \times $ (8 + 5)
                                    = (7) $ \times $ (13)
                                    = 91
Therefore, the lateral surface area of this cuboid is 91 sq. cm.
Now, let us find the total surface area of this given cuboid.
Total surface area of a cuboid = $ 2\left( lb+bh+lh \right) $
                                                      = $ 2\left[ \left( 8\times 5 \right)+\left( 5\times 3.5 \right)+\left( 8\times 3.5 \right) \right] $
Let us first solve the operations inside the circular parentheses, we get
Total surface area of a cuboid = $ 2\left[ \left( 40 \right)+\left( 17.5 \right)+\left( 28 \right) \right] $
Now, let us add them together and finally multiply by 2 to get the value of the total surface area.
Total surface area = \[2\left[ 85.5 \right]\]
                                 = 171
Therefore, the total surface area of this given cuboid is 171 sq. cm.
Hence, the lateral surface area and the total surface area of the cuboid is 91 sq. cm. and 171 sq. cm. respectively.

Note: In this question, always remember to input the units of the obtained result and the given values. The lateral surface areas are just the vertically straight walls like structure in a cuboid. In total surface area we need to consider the top and the bottom area as well.