Question

A rectangular tank is 120 centimeters long, \(x\) centimeters wide, and 70 centimeters deep. It can hold 840,000 cubic centimeters of water when full. Find the total surface area of the rectangular prism.

Answer 1

Let's draw a rectangular prism with the dimensions given in the question.
Given:
Length of the rectangular prism (l) = 120 cm

Width of the rectangular prism (b) = x cm

Height of the rectangular prism (h) = 70 cm

Volume of the rectangular prism = 840,000 cu cm.

We know that the volume of the rectangular prism \(= l \times b \times h\)
\(\Rightarrow 840000=120 \times x \times 70\)
\(\Rightarrow x=\dfrac{840000}{120 \times 70}=100\) cm

Hence, width of the rectangular prism (b) = x = 100 cm.

We know that the total surface area of the rectangular prism \(= 2 \times (lb+bh+hl)\)
\(=2\times(120\times 100+100\times 70+70\times 120)\)
\(=2\times (12000+7000+8400)\)
\(=2\times(12000+7000+8400)\)
\(=2\times 27400=54800 sq cm\)