Question

Ex. 4. A beam 9 m long, 50 cm wide and 20 cm deep is made of wood which weighs 30 kg per mº, find the weight
of the beam.

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Answer 1

• Given

• Dimensions of a beam :-
• Length of the beam = 9 m
• Breadth of the beam = 50 cm
• Height of the beam = 20 cm

• To find

• Weight of the beam

★ Concept

• Firstly, we will make all the units same.
• Then we will find the volume of the beam.
• Then we will multiply the volume by 30 kg to find the weight of the beam.

★ Formula to be used -

• Volume = l × b × h

• Solution

• Breadth of the beam = 50 cm

As we know,

★ 1 cm = 0.01 m

• Divide the given value by 100 metre.

⟶ Length = 50/100 = 0.5 m

• Height of the beam = 20 cm

⟶ Height = 20/100 = 0.2 m

Using formula,

★ Volume of the beam = l × b × h

where,

• l = length of the beam
• b = breadth of the beam
• h = height of the beam

Substituting the values,

⟶ 9 × 0.5 × 0.2

⟶ 0.9 metre cube

• Volume of the beam = 0.9 metre cube.

Weight per cubic metre = 30 kg

Weight per 0.9 metre cube = 30 × 0.9 = 27 kg

★ Therefore, Weight of the beam = 27 kg.

Answer 2

Question :-

• A beam 9 m long, 50 cm wide and 20 cm deep is made of wood which weighs 30 kg per mº, find the weight of the beam.

Given :-

• Length of Beam = 9m
• Breadth of Beam = 50cm = 0.5m
• Height of Beam = 20cm = 0.2m
• Weight per Cubic metre = 30kg

To Find :-

• What is the Weight of the Beam ?

Solution :-

${:} \longrightarrow \bf \underline{\boxed{\sf{Volume \: = \: Length \: \times \: Breadth \: \times \: Height }}}$

$\longmapsto \sf{\sf{ \: Volume \: = \: 9 \: \times \:0.5 \: \times \: 0.2 }}$

$\longmapsto \sf{\sf{ \: Volume \: = \:0.9 }}$

Volume of Beam = 9m³

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Weight per Cubic metre = 30kg ( given )

$\longmapsto \sf Weight\: per\: 0.9\: cubic\: metre\: =\: 30 \: \times \: 0.9$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Weight \: of \: beam \: = \underline {\underline{ 27kg}}}\\\end{gathered}\end{gathered}$

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