Question

A cylinder and a cone are shown below.

A cylinder with height 12 inches and volume 2,512 inches cubed. A cone with height 12 inches and volume 1,256 inches cubed.

Which explains whether the bases of the cylinder and the cone have the same area?

Answer 1

$i) Given \: height \: of \: the \: cylider (H) \\= 12\: inches$

$Let \: radius \: of \: the \: base = R \: inches$

$Volume (V) = 2512\: ( inches )^{3} \: ( given )$

$\implies \pi R^{2} H = 2512$

$\implies \pi R^{2} \times 12 = 2512$

$\implies R^{2} = \frac{ 2512 }{ 12 \pi } \: --(1)$

$ii) Given \: height \: of \: the \: cone (h) \\= 12\: inches$

$Let \: radius \: of \: the \: base = r \: inches$

$Volume (V) = 1256\: ( inches )^{3} \: ( given )$

$\implies \frac{1}{3} \times \pi r^{2} h = 1256$

$\implies\frac{1}{3}\times \pi r^{2} \times 12 = 1256$

$\implies r^{2} = \frac{ 1256 \times 3 }{ 12 \pi }$

$\implies r^{2} = \frac{ 3768 }{ 12 \pi } \: --(2)$

/* From (1) and (2), we conclude that */

$\pink { R^{2} \neq r^{2}}$

$\implies R \neq r$

$\therefore Areas \: of \: cylider \: and \: cone \\are \: not \: equal .$

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