Question

The height of the solid cone is 12cm and the area of the base is 81 π sqcm , find the curved surface area of the cone.[Take π =3.14]​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Height of solid cone, h = 12 cm

• Area of the base = 81 π sq. cm.

As we know, base of cone is circular.

Let assume that

• Radius of base = r cm

As it is given that,

$\rm \: Area_{(Base)} = 81 \: \pi$

$\rm \: \pi {r}^{2} = 81 \: \pi$

$\rm \: {r}^{2} = 81$

$\rm \: {r}^{2} = {9}^{2}$

$\rm\implies \:r \: = \: 9 \: cm$

Now, Let assume that

• Slant height of cone = l cm

We know, slant height l, height h and radius r is connected by the relationship

$\rm \: {l}^{2} \: = \: {h}^{2} + {r}^{2}$

$\rm \: {l}^{2} \: = \: {12}^{2} + {9}^{2}$

$\rm \: {l}^{2} \: = \: 144 + 81$

$\rm \: {l}^{2} \: = \: 225$

$\rm \: {l}^{2} \: = \: {15}^{2}$

$\rm\implies \:l \: = \: 15 \: cm$

Now, we know

Curved Surface Area of cone of radius r and slant height l is given by

$\boxed{ \rm{ \:CSA_{(Cone)} \: = \: \pi \: r \: l \: }}$

So, on substituting the values, we get

$\rm \: CSA_{(Cone)} = 3.14 \times 9 \times 15$

$\rm\implies \:\boxed{ \rm{ \:CSA_{(Cone)} \: = \: 423.90 \: {cm}^{2} \: \: }}$

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

Additional information :-

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

Answer 2

Answer:

The height of the solid cone is 12cm and the area of the base is 81 π sqcm , find the curved surface area of the cone.[Take π =3.14]The height of the solid cone is 12cm and the area of the base is 81 π sqcm , find the curved surface area of the cone.[Take π =3.14]The height of the solid cone is 12cm and the area of the base is 81 π sqcm , find the curved surface area of the cone.[Take π =3.14]

Step-by-step explanation:

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