Question

The slant height and the height of the cone are 28m and 21m respectively .Find the volume of the cone

Answer 1

slant height=√h²+r²

so, l²=h²+r²

r²=l²-h²⇒r²=(28)²-(21)²⇒r²=784-441=343m

volume of cone =1/3*π*r²*h=1/3*22/7*343*21=7546m²

Answer 2

Answer:

$\boxed{\sf \: Volume_{(Cone)} = 7546 \: {cm}^{3} \: }$

Step-by-step explanation:

Given that,

Height of a cone, h = 21 cm

Slant height of a cone, l = 28 cm

Let assume that r be the radius of cone.

We know, Volume of cone of radius r and height h is given by

$\sf \: Volume_{(Cone)} = \dfrac{1}{3}\pi {r}^{2}h$

can be further rewritten as

$\sf \: Volume_{(Cone)} = \dfrac{1}{3}\pi ({l}^{2} - {h}^{2}) h$

$\sf \: Volume_{(Cone)} = \dfrac{1}{3} \times \dfrac{22}{7} ({28}^{2} - {21}^{2}) \times 21$

$\sf \: Volume_{(Cone)} = 22 \times (784 - 441) \times 1$

$\sf \: Volume_{(Cone)} = 22 \times 343$

$\implies\sf \: \sf \: Volume_{(Cone)} = 7546 \: {cm}^{3}$

$\rule{190pt}{2pt}$

Additional Information

$\begin{gathered} \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$