Question

1. which of the following geometric shapes have the same volume? select each shape that has the same volume. a. a sphere with a radius of 3 cm. b. a cylinder with a radius of 8 cm and a height of 11 cm. c. a hemisphere with a radius of 5 cm. d. a cone with a radius of 5 cm and a height of 10 cm.

Explanation:

Step1: Calculate the volume of the sphere

The volume formula of a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\). Given \(r = 3\space cm\), then \(V_{sphere}=\frac{4}{3}\pi\times3^{3}=36\pi\space cm^{3}\).

Step2: Calculate the volume of the cylinder

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\). Given \(r = 8\space cm\) and \(h = 11\space cm\), then \(V_{cylinder}=\pi\times8^{2}\times11 = 704\pi\space cm^{3}\).

Step3: Calculate the volume of the hemisphere

The volume formula of a hemisphere is \(V_{hemisphere}=\frac{2}{3}\pi r^{3}\). Given \(r = 5\space cm\), then \(V_{hemisphere}=\frac{2}{3}\pi\times5^{3}=\frac{250}{3}\pi\space cm^{3}\).

Step4: Calculate the volume of the cone

The volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). Given \(r = 5\space cm\) and \(h = 10\space cm\), then \(V_{cone}=\frac{1}{3}\pi\times5^{2}\times10=\frac{250}{3}\pi\space cm^{3}\).

Answer:

C. A hemisphere with a radius of 5 cm; D. A cone with a radius of 5 cm and a height of 10 cm.