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Given the cone dimensions below: cone's slant height =20m cone's radius =12m Find the height of the cone and the cone's volume. cone height = qquad cone volume =

Given the cone dimensions below:\newlinecone's slant height =20 m =20 \mathrm{~m} \newlinecone's radius =12 m =12 \mathrm{~m} \newlineFind the height of the cone and the cone's volume.\newlinecone height = = \qquad \newlinecone volume = =

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Q. Given the cone dimensions below:\newlinecone's slant height =20 m =20 \mathrm{~m} \newlinecone's radius =12 m =12 \mathrm{~m} \newlineFind the height of the cone and the cone's volume.\newlinecone height = = \qquad \newlinecone volume = =
  1. Calculate Height using Pythagorean Theorem: Calculate the height of the cone using the Pythagorean theorem in the right triangle formed by the radius, height, and slant height of the cone.\newlineHeight h h can be found using h=l2−r2 h = \sqrt{l^2 - r^2} where l=20 l = 20 m (slant height) and r=12 r = 12 m (radius).\newlineCalculation: h=202−122=400−144=256=16 h = \sqrt{20^2 - 12^2} = \sqrt{400 - 144} = \sqrt{256} = 16 m.
  2. Calculate Volume using Formula: Calculate the volume of the cone using the formula V=13πr2h V = \frac{1}{3} \pi r^2 h where r=12 r = 12 m and h=16 h = 16 m.\newlineCalculation: V=13π(12)2(16)=13π(144)(16)=13π2304=768π V = \frac{1}{3} \pi (12)^2 (16) = \frac{1}{3} \pi (144) (16) = \frac{1}{3} \pi 2304 = 768 \pi m³.

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