Question

a cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.
20 cm
8 cm
what is the approximate volume of the tube? round to the nearest whole cubic centimeter.
1,005 cm³
1,340 cm³
3,351 cm³
4,021 cm³

Explanation:

Step1: Find the radius

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given the diameter \(d = 8\) cm, the radius \(r=\frac{d}{2}\). So \(r=\frac{8}{2}=4\) cm.

Step2: Substitute values into the volume formula

We know \(h = 20\) cm and \(r = 4\) cm. Substitute into \(V=\pi r^{2}h\). Then \(V=\pi\times(4)^{2}\times20\). First calculate \((4)^{2}=16\), so \(V=\pi\times16\times20\). Then \(16\times20 = 320\), so \(V = 320\pi\). Taking \(\pi\approx3.14\), we have \(V\approx320\times3.14\).

Step3: Calculate the value

\(320\times3.14=(300 + 20)\times3.14=300\times3.14+20\times3.14=942+62.8 = 1004.8\approx1005\)

Answer:

\(1,005\mathrm{cm}^{3}\)