Examkin

Question

Difficulty: MediumRectangular Volume and Container Capacity

A rectangular fuel holding tank at an aviation depot is 1515 feet long and 1010 feet wide. The tank currently holds 900900 cubic feet of aviation fuel, which fills it to exactly half of its total capacity. What is the total interior height of the tank, in feet?

Answer: 12 feet

Answer

The total interior height of the tank is 1212 feet.
By first finding the base area (15×10=15015 \times 10 = 150 sq ft), we can determine how high 900900 cubic feet of fuel reaches by dividing the volume by the area (900÷150=6900 \div 150 = 6 feet). Because the tank is half full, the 66-foot depth is exactly half of the tank's total height, making the total height 1212 feet.

Step-by-Step Solution

1
Calculate the area of the rectangular base of the tank.
15 ft×10 ft=150 sq ft15 \text{ ft} \times 10 \text{ ft} = 150 \text{ sq ft}
The volume of a rectangular prism is the product of its base area and height. Finding the base area is the first step to isolating the height.
2
Calculate the current depth of the aviation fuel.
900 cu ft÷150 sq ft=6 ft900 \text{ cu ft} \div 150 \text{ sq ft} = 6 \text{ ft}
Dividing the current volume of the fuel by the base area of the tank yields the height (depth) of the liquid currently inside.
3
Calculate the total interior height of the tank.
6 ft×2=12 ft6 \text{ ft} \times 2 = 12 \text{ ft}
The problem states the tank is exactly half full, meaning the total interior height is twice the depth of the current fuel level.

Key Concept

Calculating a missing dimension of a rectangular prism using volume and partial capacity
Rate this question

Topics

Rectangular Volume and Container Capacity

More questions from this topic