Question

1. find the volume of a cone to the nearest cm³ with a diameter of 6 cm and a slant height of 5 cm. hint: recall that you can use the pythagorean theorem to find slant height, height, or radius of the cone. we know

Explanation:

Step1: Find the radius

The diameter $d = 6$ cm, so the radius $r=\frac{d}{2}=\frac{6}{2}=3$ cm.

Step2: Find the height of the cone

Using the Pythagorean theorem $l^{2}=h^{2}+r^{2}$, where $l = 5$ cm (slant - height) and $r = 3$ cm. Then $h=\sqrt{l^{2}-r^{2}}=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4$ cm.

Step3: Calculate the volume of the cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3$ cm and $h = 4$ cm into the formula: $V=\frac{1}{3}\pi\times3^{2}\times4=\frac{1}{3}\pi\times9\times4 = 12\pi\approx12\times3.14 = 37.68\approx38$ $cm^{3}$.

Answer:

$38$ $cm^{3}$