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
fish tank
10 in.
10 in.
40 in²
30 in.
20 in.
(not drawn to scale)
a 560 in³
b 10 in³
c 59,600 in³
d 5600 in³

Explanation:

Step1: Calculate the volume of the vase

The volume \(V\) of a rectangular prism is given by \(V = \text{Base Area}\times\text{Height}\). For the vase, the base area \(B = 40\space in^{2}\) and height \(h=10\space in\). So, \(V_{vase}=40\times10 = 400\space in^{3}\).

Step2: Calculate the volume of the fish - tank

The base area of the fish - tank \(B_{fish - tank}=\text{length}\times\text{width}\). Here, length \(l = 30\space in\) and width \(w = 20\space in\), so \(B_{fish - tank}=30\times20=600\space in^{2}\), and height \(h = 10\space in\). Then \(V_{fish - tank}=600\times10=6000\space in^{3}\).

Step3: Calculate the additional water needed

The additional water needed \(V = V_{fish - tank}-V_{vase}\). Substitute \(V_{fish - tank}=6000\space in^{3}\) and \(V_{vase}=400\space in^{3}\) into the formula: \(V=6000 - 400=5600\space in^{3}\).

Answer:

D. \(5600\space in^{3}\)