Question

QuestiuI4

12 PL3
If a rectangular prism has a volume of 550 cm and its dimension are all tripled,
then what would be the new volume?
New volume

Answer 1

New volume = 27 × 550 = 14850 cm³

Explanation:

volume of a rectangular prism = L × B × H

where

L = length

B = Breadth

H = height

The initial volume = 550 cm³

LBH = 550 cm³

The new volume when all the dimensions are tripled

3L, 3B and 3H.

3L × 3B × 3H = 27LBH

Therefore,

27LBH = 27(550)

New volume = 27 × 550 = 14850 cm³

Answer 2

The new volume is 14,850cm³

Explanation:

Given

Volume of a rectangular prism = 550cm

Required

Value of volume when the dimensions are tripled.

The volume of a rectangular prism is calculated using the following formula.

V = lbh

When Volume = 550, the formula is written as follows

550 = lbh

Rearrange

lbh = 550

However, when each dimension is tripled.

This means that,

new length = 3 * old length

new breadth = 3 * old breadth

new height = 3 * old height

Let L, B and H represent the new length, new breadth and new height respectively

In other words,

L = 3l

B = 3b

H = 3h

Calculating new volume

New volume = LBH

Substitute, 3l for L, 3b for B and 3h for H;

V = 3l * 3b * 3h

V = 3 * l * 3 * b * 3 * h

V = 3 * 3 * 3 * l*b*h

V = 27 * lbh

Recall that lbh = 550

So,

V = 27 * 550

V = 14,850

Hence, the new volume is 14,850cm³