Question

calculate the height of a cylinder with radius 3 cm and volume 1187 cm³. a) 126 cm b) 396 cm c) 42 cm d) 20 cm

Explanation:

Step1: Recall volume formula for cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(V\) is volume, \(r\) is radius and \(h\) is height. We need to solve for \(h\), so we can rewrite the formula as \(h = \frac{V}{\pi r^{2}}\).

Step2: Substitute given values

Given \(V = 1187\ cm^{3}\) and \(r = 3\ cm\). Substitute into the formula: \(h=\frac{1187}{\pi\times3^{2}}=\frac{1187}{9\pi}\). Using \(\pi\approx3.14\), we have \(h=\frac{1187}{9\times3.14}=\frac{1187}{28.26}\approx42\ cm\)

Answer:

c) 42 cm