Question

a vase is in the shape of a rectangular prism. it has a base area of 40 square inches and a height of 10 inches. the vase is filled to the top with water and emptied into a fish tank. the fish tank is also shaped like a rectangular prism. how much more water would be needed to fill the fish tank to the top? vase 10 in. 40 in² fish tank 10 in. 30 in. 20 in. (not drawn to scale) a 560 in³ b 10 in³ c 59,600 in³ d 5600 in³

Explanation:

Step1: Calculate volume of vase

The volume formula for a rectangular - prism is $V = B\times h$, where $B$ is the base area and $h$ is the height. For the vase, $B = 40$ square inches and $h = 10$ inches. So, $V_{vase}=40\times10 = 400$ cubic inches.

Step2: Calculate volume of fish - tank

For the fish - tank, which is also a rectangular prism with length $l = 30$ inches, width $w = 20$ inches and height $h = 10$ inches. Using the volume formula $V=l\times w\times h$, we have $V_{tank}=30\times20\times10=6000$ cubic inches.

Step3: Calculate remaining volume

The amount of additional water needed to fill the fish - tank is the difference between the volume of the fish - tank and the volume of the vase. Let $V$ be the additional volume. Then $V = V_{tank}-V_{vase}=6000 - 400=5600$ cubic inches.

Answer:

D. 5600 in³