Question

A rectangular prism has a volume of 840 in.³ the height of the prism at 6 inches and the width is 10 inches find the length of the prison and explain how you found it

Answer 1

Given

Volume of Rectangular prism = 840 inch ³

Height of the prism = 6 inches

breadth of the prism = 10 inches

To Find

We have to find its length

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Since, the prism is in the shape of Rectangle and have height ,breadth & length so ,it will be the cuboid.We have given breadth ,height and volume of cuboid and have to find its length. So,in order to find length we would apply formula for volume of cuboid.

Volume of cuboid = ℓ×Ъ×н

Where ℓ = length

$\:\:\:\:\:\:\:\:\:\:$Ъ=breadth

$\&\:\:\:\:\:\:\:\:\:\:$н=height

➙Volume of cuboid= 840

➙length ×10×6= 840

➙ℓ× 60= 840

➙ℓ= 840÷60

➙ℓ= 84/6=14

Hence,length of the prism is 14 inches

Check:

Volume of cuboid= 14×10×6

Volume of cuboid= 140×6= 840 in.³

Answer 2

Given:

A rectangular prism has a volume of 840 in.³

To Find:

length of the rectangular prism.

Solution:

A right rectangle prism has 6 faces, all rectangular in shape. The angles between the base and sides are right angles. Each is a right angle. Also called a cuboid

We know that

$Volume \: of \: Cuboid = l \times b \times h$

here we have

Width = 10 inches

Height =6 inches

According to question

$Volume \: of \: cuboid = l \times 10 \times 6$

$= 840 {m}^{3} = 60 \times l$

$= \frac{840}{60} = l$

= > 14 = Length

Hence, the value of its Length is 14 inches