Question

The dimensions of a cuboid are in the ratio of 3 : 2 : 1 and the total surface area is 198 square cm . find its volume

answer is 162 cubic meters
l want process

Answer 1

Hello.......^_^

here is your answer.......

Given :-

dimension of a cuboid are in ratio 3:2:1

total surface area = 198

Let length ( l ) = 3x

breadth( b) = 2x

height ( h ) = 1x

total surface area = 2 ( lb+ bh+hl )

$= 198 = 2( lb+ bh +hl ) \\ = 198 = 2(3x \times 2x + 2x \times 1x + 1x \times 3x) \\ = 198 = 2(6 {x}^{2} + 2 {x}^{2} + 3 {x}^{2} ) \\ = 198 = 2(11 {x)}^{2} \\ = 198 = 22 {x}^{2} \\ = \frac{198}{22} = {x}^{2} \\ = 9 = {x}^{2} \\ = \sqrt{9 } = x \\ = 3 = x$

$so \\ length = 3x = 3 \times x = 3 \times 3 = 9 \\ breadth = 2x = 2 \times x = 2 \times 3 = 6 \\ height = 1x = 1 \times x = 1 \times 3 = 3$

length =9 cm

breadth = 6 cm

height = 3 cm

$volume = l \times b \times h \\ = 9 \times 6 \times 3 \\ = 54 \times 3 \\ = 162 {cm}^{3}$

hope this helps............ ^_^

Answer 2

Answer:

It is very helpful. Thank you