Question

The dimensions of a cuboid are in ratio 3:2:1 find the dimensions of the cuboid if it's volume is 48 cubic cm​

Answer 1

Correct Question:-

The dimensions of a cuboid are in ratio 3:2:1 find the dimensions of the cuboid if it's volume is 48 cm³.

Given:-

• Ratio of dimensions = 3:2:1
• Volume of cuboid = 48 cm³

To Find:-

• Dimensions of cuboid

Solution:-

Put x in the ratio,

• Length of cuboid = 3x
• Breadth of cuboid = 2x
• Height of cuboid = x

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: volume \: of \: cuboid}}}$

$\boxed{ \mathfrak{ \purple{ \star \: \: \: \: { \large{ \red{volume = length \times breadth \times height}}}}}}$

According to question,

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: \:3x \times 2x \times x = 48}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: \:6 {x}^{3} = 48}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: \: {x}^{3} = \frac{48}{6} }$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: \: {x}^{3} = 8}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: \:x = \sqrt[3]{8} }$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \: { \boxed{\mathfrak{ \blue{x = 2}}}}} \star$

Now,

• Length of cuboid = 3x = 6 cm
• Breadth of cuboid = 2x = 4 cm
• Height of cuboid = x = 2 cm

Hence,

• The dimensions of cuboid are 6 cm,4 cm and 2 cm

Answer 2

Answer:

Hi

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