Question

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively.
Find:-
» Total surface area of the cuboid
» Lateral surface area of the cuboid

Answer 1

★ Given:-        

• ➺ Length of the cuboid = 5m
• ➺ Breadth of the cuboid = 4m
• ➺ Height of the cuboid = 3m

★ To find:-      

• ➺ Total surface area of the cuboid
• ➺ Lateral surface area of the cuboid

★ Solution:-      

Here, we have given that the rooms length, breadth and height of a room are 5 m, 4 m and 3 m respectively.

So firstly we will find out the total surface area of the cuboid by using the formula.

                     ____________

✷ Total surface area of the cuboid ✷

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:(\:lb\:+\:bh\:+\:hl)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:(\:5\:\times\:4\:+\:4\:\times\:3\:+\:3\:\times\:5\:)\:}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:(\:20\:+\:12\:+\:15\:)\:}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:(\:47\:)\:}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\times\:47\:}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:CUBOID\:)}\:=\:94\:m^{2}}$

. ° . The total surface area of the cuboid room is 94 m².

                               ______________

✷ Lateral surface area of the cuboid ✷

$\qquad\tt{:\implies\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2h\:(\:l\:+\:b\:)}$

$\qquad\tt{:\implies\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\times\:3\:(\:5\:+\:4\:)}$

$\qquad\tt{:\implies\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\times\:3\:(\:9\:)}$

$\qquad\tt{:\implies\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:6\:\times\:9\:}$

$\qquad\tt{:\implies\:Lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:54\:m^{2}\:}$

. ° . The lateral surface area of the cuboid room is 54 m².

                             __________

Answer 2

Given that:- For a cuboid,

» Length is $5m$,

» Breadth is $4m$,

» Height is $3m$

To find:-

» Total surface area of the cuboid

» Lateral surface area of the cuboid

Solution:-

So first we have to find out the total surface area of the cuboid,

For that, we have the formula,

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

Now, by putting the given values, in the formula

$=>2(5\times4+4\times 3+3\times 5)$

$=>2(20+12+15)$

$=>2(47)$

$=>94m^2$

Therefore, the total surface area of a cuboid is $94m^2.$

Now we have to find the lateral surface area of the cuboid,

For that, we have the formula,

The lateral surface area of the cuboid $=2h(l+b)$

By putting the given values, in the formula

$=>2\times 3(5+4)$

$=>6(9)$

$=>54m^2$

Hence, the lateral surface area of the cuboid is $54m^2.$