Question

A storage shed is a rectangular prism and has dimensions of 6 meters by 5 meters by 12 meters. if jean double these dimensions, she believes that only is double the volume. are you correct?

Answer 1

That is false. I would be eight times as much volume than before.

Answer 2

If Jean double these dimensions, the volume will be eight times the initial volume.

Further explanation

To solve the above questions, we need to recall some of the formulas as follows:

Volume of Prism = Base Area × Height

Area of Square = (Side Length)²

Let us now tackle the problem !

Given:

A rectangular prism has dimensions of L = 6 meters by W = 5 meters by H = 12 meters.

If Jean double these dimensions , then:

$\texttt{Initial Volume} : \texttt{Final Volume} = (L \times W \times H) : (2L \times 2W \times 2H)$

$\texttt{Initial Volume} : \texttt{Final Volume} = (L \times W \times H) : (8 \times L \times W \times H)$

$\texttt{Initial Volume} : \texttt{Final Volume} = 1 : 8$

$\texttt{Final Volume} = \boxed {8 \times \texttt{Initial Volume}}$

Conclusion:

If Jean double these dimensions, the volume will be eight times the initial volume.

Initial Volume = 6 × 5 × 12 = 360 m³

Final Volume = 2(6) × 2(5) × 2(12) = 8 × 360 m³ = 2880 m³

Learn more

• The perimeter of a polygon : https://brainly.com/question/6361596
• The perimeter of a rectangle : https://brainly.com/question/7619923
• The perimeter of a triangle : https://brainly.com/question/2299951

Answer details

Grade: College

Subject: Mathematics

Chapter: Three Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width