Question

Example 1:
The dimensions of a cuboid are in the ratio 3:2:1 and the total surface area is 5632 cm?
Find its volume.
Solution:​

Answer 1

Question :

The dimensions of a cuboid are in the ratio 3:2:1 and the total surface area is 5632 cm² .Find its volume ?

Answer :

$\sf\pink{Given:}$

• Ratio of dimension of cuboid is 3 : 2 : 1

• Total surface area of the cuboid is 5632 cm² .

$\sf\pink{To\:find:}$

• volume of the cuboid ?

Explanation :

To find the volume we first need to find the height , breadth and length of the cuboid that it's dimensions . We can find it using the formula of total surface area of cuboid .

• let the length be 3x .

• let the breadth be 2x .

• let the height be x .

$\sf\red{Total\: surface\:area\:of\:cuboid = 2 ( lb + bh + hl )}$

$\\ \longrightarrow\sf{ 5632 = 2\times ( 3x\times 2x + 2x\times x + x\times 3x )}$

$\\ \longrightarrow\sf{ 5632 = 2\times ( 6{x}^{2} + 2{x}^{2} + 3{x}^{2})}$

$\\ \longrightarrow\sf{ 5632 = 2\times [(6 + 2 + 3 ){x}^{2}]}$

$\\ \longrightarrow\sf{ 5632 = 2\times [(8 + 3 ){x}^{2}]}$

$\\ \longrightarrow\sf{ 5632 = 2\times 11 {x}^{2}}$

$\\ \longrightarrow\sf{ 5632 = 22{x}^{2}}$

$\\ \longrightarrow\sf{\dfrac{5632}{22}= {x}^{2}}$

$\\ \longrightarrow\sf{256 = {x}^{2}}$

$\\ \longrightarrow\sf{x = \sqrt{256}}$

$\\ \longrightarrow\sf{x = 16}$

• length is 3x.

$\\ \longrightarrow\sf{3\times 16}$

$\\ \longrightarrow\sf{48}$

Therefore the length is 48 cm.

• breadth is 2x .

$\\ \longrightarrow\sf{2\times 16}$

$\\ \longrightarrow\sf{32}$

Therefore the breadth is 32 cm.

• height is x

$\\ \longrightarrow\sf{16}$

Therefore the height is 16 cm

$\sf\purple{ Volume\:of\: cuboid = l\times b\times h }$

$\\ \longrightarrow\sf{48\times 32\times 16}$

$\\ \longrightarrow\sf{1536\times 16}$

$\\ \longrightarrow\sf{24576}$

Therefore the volume is 24576 cm³