Question

which cone has a volume of 24π cm³?

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for a cone is \( V=\frac{1}{3}Bh\) (where \( B\) is the base - area and \( h\) is the height) or \( V = \frac{1}{3}\pi r^{2}h\) (when using the radius \( r\) of the base).

Step2: Calculate the volume for each cone

First cone:

Given \( r = 8\div2=4\mathrm{cm}\), \( h = 4.5\mathrm{cm}\).
Using \( V=\frac{1}{3}\pi r^{2}h\), we have \( V=\frac{1}{3}\pi\times4^{2}\times4.5=\frac{1}{3}\pi\times16\times4.5 = 24\pi\mathrm{cm}^{3}\).

Second cone:

Given \( B = 25\mathrm{cm}^{2}\), \( h = 3.5\mathrm{cm}\).
Using \( V=\frac{1}{3}Bh\), we have \( V=\frac{1}{3}\times25\times3.5=\frac{87.5}{3}\pi\mathrm{cm}^{3}\approx29.17\pi\mathrm{cm}^{3}\).

Third cone:

Given \( r = 3\mathrm{cm}\), \( h = 6.5\mathrm{cm}\).
Using \( V=\frac{1}{3}\pi r^{2}h\), we have \( V=\frac{1}{3}\pi\times3^{2}\times6.5=\frac{1}{3}\pi\times9\times6.5 = 19.5\pi\mathrm{cm}^{3}\).

Fourth cone:

Given \( B = 4\pi\mathrm{cm}^{2}\), \( h = 7.5\mathrm{cm}\).
Using \( V=\frac{1}{3}Bh\), we have \( V=\frac{1}{3}\times4\pi\times7.5 = 10\pi\mathrm{cm}^{3}\).

Answer:

The first cone has a volume of \( 24\pi\mathrm{cm}^{3}\).