Question

use the appropriate volume formula to match each object to its correct volume. leave your answers in terms of π. answer choices. drag the answer choices to the correct category over here! a cone with radius 4 cm and height 9 cm a cylinder with radius 5 cm and height 3 cm a sphere with radius 4 cm a rectangular prism with length 7 cm, width 3 cm, and height 4 cm

Explanation:

Step1: Volume of cone formula

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 4\mathrm{cm}\) and \(h=9\mathrm{cm}\), substitute into the formula: \(V=\frac{1}{3}\pi\times4^{2}\times9\).

Step2: Calculate cone volume

First, \(4^{2}=16\), then \(\frac{1}{3}\times16\times9 = 48\). So the volume of the cone is \(48\pi\mathrm{cm}^{3}\).

Step3: Volume of cylinder formula

The volume formula for a cylinder is \(V=\pi r^{2}h\). Given \(r = 5\mathrm{cm}\) and \(h = 3\mathrm{cm}\), substitute into the formula: \(V=\pi\times5^{2}\times3\).

Step4: Calculate cylinder volume

First, \(5^{2}=25\), then \(25\times3=75\). So the volume of the cylinder is \(75\pi\mathrm{cm}^{3}\).

Step5: Volume of sphere formula

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 4\mathrm{cm}\), substitute into the formula: \(V=\frac{4}{3}\pi\times4^{3}\).

Step6: Calculate sphere volume

First, \(4^{3}=64\), then \(\frac{4}{3}\times64=\frac{256}{3}\). So the volume of the sphere is \(\frac{256}{3}\pi\mathrm{cm}^{3}\).

Step7: Volume of rectangular prism formula

The volume formula for a rectangular prism is \(V=l\times w\times h\). Given \(l = 7\mathrm{cm}\), \(w = 3\mathrm{cm}\) and \(h = 4\mathrm{cm}\), substitute into the formula: \(V=7\times3\times4\).

Step8: Calculate rectangular prism volume

\(7\times3\times4=84\). So the volume of the rectangular prism is \(84\mathrm{cm}^{3}\).

Answer:

• A cone with radius \(4\mathrm{cm}\) and height \(9\mathrm{cm}\): \(48\pi\mathrm{cm}^{3}\)
• A cylinder with radius \(5\mathrm{cm}\) and height \(3\mathrm{cm}\): \(75\pi\mathrm{cm}^{3}\)
• A sphere with radius \(4\mathrm{cm}\): \(\frac{256}{3}\pi\mathrm{cm}^{3}\)
• A rectangular prism with length \(7\mathrm{cm}\), width \(3\mathrm{cm}\), and height \(4\mathrm{cm}\): \(84\mathrm{cm}^{3}\)