Question

The volume of a cuboid is 972m. If its length and breadth are 12m and 9m
respectively, find its height.

Answer 1

Given -

• Volume of cuboid is 972 m³

• Length of cuboid is 12 m

• Breadth of cuboid is 9 m

To find -

• Cuboid's height

Formula used -

• Volume of cuboid = L × B × H

Solution -

In the Question, we are provided with the volume, length and breadth of the cuboid, and we need to find it's height. For that, we will apply,the formula of volume of cuboid, place the values given, and then, we will solve the further question. Let's do it!

According to question -

• Volume, v = 972 m³

• Length, l = 12 m

• Breadth, b = 9 m

• Height = h

Volume of cuboid -

• L × B × H

On substituting the values -

$\sf \longrightarrow \: v \: = \: l \: \times \: b \: \times \: h \\ \\ \sf \longrightarrow \: 972 { \: m}^{3} \: = \: 12 \: m \: \times \: 9 \: m \: \times \: h \\ \\ \sf \longrightarrow \: 972 { \: m}^{3} \: = \: 108 \: m \: \times \: h \\ \\ \sf \longrightarrow \: h \: = \cancel \dfrac{972 \: m}{108 \: m} \\ \\ {\longrightarrow {\boxed {\sf \therefore \: {\: h \: = 9 \: m}}}}$

Verification -

$\sf \longrightarrow \: v \: = \: l \: \times \: b \: \times \: h \\ \\ \sf \longrightarrow \: 972 { \: m}^{3} = \: 12 \: m \: \times \: 9 \: m \: \times \: 9 \: m \\ \\ \sf \longrightarrow \: 972 {m}^{3} \: = \: 972 { \: m}^{3}$

Hence, verified!

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Answer 2

Given : The volume of a cuboid is 972m. And it's length and breadth are 12m and 9m.

To Find : Height of the cuboid.

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Here, length of the cuboid is 12m and breadth is 9m. The volume of the cuboid is 972m. Firstly we'll put the given values in the volume of the cuboid formula. Then we'll get the value of height of the cuboid.

$\:$

For finding the volume of a cuboid, formula is given as -

$\: \:$

$\star \: \underline{\boxed{\sf\pink{Volume_{(cuboid) } = l \times b \times h}}}$

$\:$

❍ Where, l denotes length, b denotes breadth and h denotes height of the cuboid.

$\:$

$\bold {\underline{According \: to \: the \: question \: :}}$

$\:$

$\sf:\implies \: Volume_{(cuboid) } = l \times b \times h \\ \\ \\ \sf:\implies \:972 = 12 \times 9 \times h \\ \\ \\ \sf:\implies \:972 = 108h \\ \\ \\ \sf:\implies \:h = \cancel \frac{972}{108} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{h = 9m}}} \: \bigstar \\ \\ \\ \\ \sf \therefore{ \underline{Hence, \: the \: volume \: of \: the \: cuboid \: is \: \bold{9m}.}}$