Question

drag the correct answer into the boxes:

Explanation:

Step1: Calculate the volume of the first cylinder

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). Given \(r = 2\mathrm{cm}\), \(h=5\mathrm{cm}\), then \(V=\pi\times2^{2}\times5=\pi\times4\times 5 = 20\pi\approx62.8\mathrm{cm}^{3}\)

Step2: Calculate the volume of the first cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 3\mathrm{cm}\), \(h = 7\mathrm{cm}\), then \(V=\frac{1}{3}\pi\times3^{2}\times7=\frac{1}{3}\pi\times9\times7=21\pi\approx65.94\mathrm{cm}^{3}\)

Step3: Calculate the volume of the first sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 4\mathrm{cm}\), then \(V=\frac{4}{3}\pi\times4^{3}=\frac{4}{3}\pi\times64=\frac{256}{3}\pi\approx267.95\mathrm{cm}^{3}\)

Step4: Calculate the volume of the second cylinder

Using \(V=\pi r^{2}h\) with \(r = 4\mathrm{cm}\), \(h = 6\mathrm{cm}\), then \(V=\pi\times4^{2}\times6=\pi\times16\times6 = 96\pi\approx301.44\mathrm{cm}^{3}\)

Step5: Calculate the volume of the second cone

Using \(V=\frac{1}{3}\pi r^{2}h\) with \(r = 2\mathrm{cm}\), \(h = 5\mathrm{cm}\), then \(V=\frac{1}{3}\pi\times2^{2}\times5=\frac{20}{3}\pi\approx20.93\mathrm{cm}^{3}\)

Step6: Calculate the volume of the second sphere

Using \(V=\frac{4}{3}\pi r^{3}\) with \(r = 3\mathrm{cm}\), then \(V=\frac{4}{3}\pi\times3^{3}=\frac{4}{3}\pi\times27 = 36\pi\approx113.04\mathrm{cm}^{3}\)

Answer:

First row (from left to right): \(62.8\mathrm{cm}^{3}\), \(65.94\mathrm{cm}^{3}\), \(267.95\mathrm{cm}^{3}\)
Second row (from left to right): \(301.44\mathrm{cm}^{3}\), \(20.93\mathrm{cm}^{3}\), \(113.04\mathrm{cm}^{3}\)