A fish tank measures 3 ft by 1.5 ft by 2 ft. It is filled with water. Water weighs 62.5 lbs per cubic ft. What is the weight of the water in the tank? Provide the answer in pounds. Do not round.
Answer (1)
Calculate the volume of the fish tank by multiplying its dimensions: V o l u m e = 3 × 1.5 × 2 = 9 ft 3 .
Multiply the volume by the weight of water per cubic foot to find the total weight: W e i g h t = 9 × 62.5 = 562.5 lbs .
The weight of the water in the tank is 562.5 lbs.
State the final answer: 562.5 lbs .
Explanation
Problem Analysis We are given a fish tank with dimensions 3 ft by 1.5 ft by 2 ft, filled with water. We also know that water weighs 62.5 lbs per cubic ft. Our goal is to find the total weight of the water in the tank.
Calculate the Volume First, we need to calculate the volume of the fish tank. The volume of a rectangular prism (which is the shape of the fish tank) is given by the formula: V o l u m e = l e n g t h × w i d t h × h e i g h t In our case, the length is 3 ft, the width is 1.5 ft, and the height is 2 ft. So, the volume is: V o l u m e = 3 f t × 1.5 f t × 2 f t = 9 f t 3
Calculate the Weight Next, we need to find the weight of the water in the tank. We know that water weighs 62.5 lbs per cubic ft. To find the total weight, we multiply the volume of the tank by the weight of water per cubic foot: W e i g h t = V o l u m e × Wa t er w e i g h t p er c u bi c f oo t W e i g h t = 9 f t 3 × 62.5 l b s / f t 3 = 562.5 l b s
Final Answer Therefore, the weight of the water in the tank is 562.5 lbs.
Examples
Understanding how to calculate the weight of water in a tank is useful in many real-world scenarios. For example, when designing a building, engineers need to calculate the weight of water tanks to ensure the structure can support the load. Similarly, aquarium enthusiasts need to know the weight of their filled tanks to ensure they are placed on a suitable stand. This calculation helps in ensuring safety and structural integrity in various applications.
