Question

A rectangular prism has a width of 3m, a length of 5m, and a height double of its length. Find its volume.
a. 75 m 3 b. 95 m 3 c. 105 m 3 d. 150 m

Answer 1

AnswEr :

• The volume of a rectangular prism is 150m³.

Explanation :

We are given with the width of the rectangular prism as well as length of a rectangular prism and the height of rectangular prism is double of its length, that is,

• Width of rectangle = 3m.
• Length of rectangle = 5m.
• Height of rectangle = Double of its length.

We are supposed to calculate the volume of a rectangular prism.

As it is given that, the height of a rectangular prism is double of its length. So,

→ Height = 2(length)

→ Height = 2(5)

→ Height = 10m.

Now we have also a height of the rectangular field, now we can easily find out the volume of a rectangular prism. So let's calculate the volume of a rectangular prism.

We know that, if we are given with the length, width and height of a rectangular prism, we have the required formula, that is,

→ Volume = Length × Width × Height

Or, Volume = L × W × H

Where we have values as :

• L = 5m.
• W = 3m.
• H = 10m.

By using the required formula and substituting all the given values in the formula, we get :

→ Volume = 5 × 3 × 10

→ Volume = 15 × 10

→ Volume = 150

Hence, the volume of a rectangular prism is 150m³. So the option (d) is the correct option for this question.

Answer 2

Answer:

Given :-

• A rectangular prism has a width of 3 m, a length of 5 m, and a height will be double of its length.

To Find :-

• What is the volume.

Formula Used :-

$\clybsuit$ Volume Of Cuboid Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Volume_{(Cuboid)} =\: Length \times Breadth \times Height}}}$

Solution :-

First, we have to find the height of a rectangular prism :

$\leadsto$ The height of a rectangular prism will be double of its length.

Given :

• Length = 5 m

$\implies \sf Height =\: 2 \times Length$

$\implies \sf Height =\: 2 \times 5\: m$

$\implies \sf\bold{\purple{Height =\: 10\: m}}$

Now, we have to find the volume of a rectangular prism :

Given :

$\bigstar\: \: \bf{Length =\: 5\: m}$

$\bigstar\: \: \bf{Width\: or\: breadth =\: 3\: m}$

$\bigstar\: \: \bf{Height =\: 10\: m}$

According to the question by using the formula we get,

$\footnotesize\longrightarrow \sf \bold{\green{Volume_{(Rectangular\: Prism)} =\: Length \times Breadth \times Height}}$

$\longrightarrow \sf Volume_{(Rectangular\: Prism)} =\: 5 \times 3 \times 10$

$\longrightarrow \sf Volume_{(Rectangular\: Prism)} =\: 15 \times 10$

$\longrightarrow \sf\bold{\red{Volume_{(Rectangular\: Prism)} =\: 150\: m}}$

${\small{\bold{\underline{\therefore\: The\: volume\: of\: rectangular\: prism\: is\: 150\: m\: .}}}}$

Hence, the correct options is option no (d) 150 m .

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IMPORTANT FORMULA :-

$\clubsuit$ Lateral Surface Area or LSA of Cuboid Formula :

$\footnotesize\: \mapsto\sf\boxed{\bold{\pink{Lateral\: Surface\: Area_{(Cuboid)} =\: 2h(l + b)}}}$

$\clubsuit$ Total Surface Area or TSA of Cuboid Formula :

$\footnotesize\mapsto\sf\boxed{\bold{\pink{Total\: Surface\: Area_{(Cuboid)} =\: 2(lb + bh + hl)}}}$

where,

• l = Length
• b = Breadth
• h = Height