Question

tiana has a cylindrical aquarium for her pet fish. the aquarium has a diameter of 10 inches and a height of 15 inches. tiana is getting more fish, and wants to buy a larger aquarium. select the aquariums that have a greater volume than the one tiana currently has. a cylindrical aquarium with a radius of 6 inches and a height of 15 inches. a spherical aquarium with a diameter of 10 inches. a square prism aquarium with side lengths of 10 inches on its base and a height of 15 inches. a cylindrical aquarium with a radius of 5 inches and a height of 16 inches.

Explanation:

Step1: Calculate the volume of Tiana's current aquarium

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). Given the diameter \(d = 10\) inches, the radius \(r=\frac{d}{2}=5\) inches and height \(h = 15\) inches.
\(V_{1}=\pi\times(5)^{2}\times15=\pi\times25\times15 = 375\pi\approx375\times3.14 = 1177.5\) cubic inches.

Step2: Calculate the volume of the first - option cylinder

For a cylinder with \(r = 6\) inches and \(h = 15\) inches. Using \(V=\pi r^{2}h\), we have \(V_{2}=\pi\times(6)^{2}\times15=\pi\times36\times15=540\pi\approx540\times3.14 = 1695.6\) cubic inches. Since \(1695.6>1177.5\).

Step3: Calculate the volume of the spherical aquarium

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(d = 10\) inches, \(r = 5\) inches.
\(V_{3}=\frac{4}{3}\pi\times(5)^{3}=\frac{4}{3}\pi\times125=\frac{500\pi}{3}\approx\frac{500\times3.14}{3}\approx523.3\) cubic inches.

Step4: Calculate the volume of the square - prism aquarium

The formula for the volume of a square - prism (rectangular prism with \(l = w\)) is \(V=l\times w\times h\). Here \(l = w=10\) inches and \(h = 15\) inches.
\(V_{4}=10\times10\times15=1500\) cubic inches. Since \(1500>1177.5\)

Step5: Calculate the volume of the fourth - option cylinder

For a cylinder with \(r = 5\) inches and \(h = 15\) inches. Using \(V=\pi r^{2}h\), we have \(V_{5}=\pi\times(5)^{2}\times15=375\pi\approx1177.5\) cubic inches.

Answer:

A. A cylindrical aquarium with a radius of 6 inches and a height of 15 inches, C. A square prism aquarium with side lengths of 10 inches on its base and a height of 15 inches.