Question

A rectagular tank is $120cm$ long, $xcm$ wide and $70cm$ depth. It can hold $840,000{\text{cm}}^3$ volume of water upto it's full capacity. Find the total surface area of the rectangular prism.

• A. $548\times {10}^2{\text{cm}}^3$
• B. $548{\text{cm}}^2$
• C. $548\times {10}^3{\text{cm}}^2$
• D. $548\times {10}^2{\text{cm}}^2$

Answer 1

The correct option is D $548\times {10}^2{\text{cm}}^2$

Let's draw a rectangular prism with dimensions given in the questions.
Given,
Length of the rectangular prism $l=120$ cm

Breadth of the rectangular prism $b=x$ cm

Height of the rectangular prism $h=70$ cm

Volume of rectangular prism $=840,000{\text{cm}}^3$

$\to$As we know,
Volume of rectangular prism $=lbh$

$840,000=120\times x\times 70$

$x=\frac{840000}{120\times 70}=100cm$

Hence, Breadth of the rectnagular prism $b=x=100$ cm

$\to$As we know
The total surface area of a rectangular prism $=2\left(lb\right)+2\left(bh\right)+2\left(lh\right)$

$=(2\times 120\times 100)+(2\times 100\times 70)+(2\times 120\times 70)$

$=24000+14000+16800=548\times {10}^2{\text{cm}}^2$

Option (d) is correct.