Question

Find the slant height and curved surface area of a cone whose volume is 12935 cu.cm and the diameter of the base is 42 cm.

Answer 1

Given :

• Diameter of base = 42 cm .
• Volume of cone = 12935 cm³

To find :

• Slant height
• Curved Surface Area

Solution :

Volume of cone is given by the formula :

$\boxed{ \tt volume = \dfrac{1}{3} \pi {r}^{2} h } \\ \\ \sf where \: r = base \: radius \: and \: h = \perp height$

Diameter = 42 cm

Radius (r) = Diameter / 2

= 42/2

= 21 cm

$\tt 12935 = \dfrac{1}{3} \times \dfrac{22}{7} \times 21 \times 21 \times h$

$\tt 12935 = 22 \times 21 \times h$

$\tt h = \dfrac{12935}{22 \times 21} \\ \\ \tt h = \frac{12395}{462} \\ \\ \tt h = 27.99 \\ \\ \boxed{ \tt h \approx28 \: cm}$

The slant height of right circular cone is given by :

$\boxed{ \tt l = \sqrt{ {r}^{2} + {h}^{2} } }$

$\tt l = \sqrt{ {21}^{2} + {28}^{2} } \\ \\ \tt l = \sqrt{441 + 784} \\ \\ \tt l = \sqrt{1225} \\ \\ \boxed{\tt l = 35 \: cm }$

The Curved surface area of cone is given by :

$\boxed{ \tt csa \: of \: cone = \pi rl}$

$= \tt\dfrac{22}{7} \times 21 \times 35 \\ \\ \tt = 22 \times 21 \times 5 \\ \\ \tt \: = 2310$

$\underline{ \sf\therefore \: the \: csa \: of \: cone \: is \: 2310 \: {cm}^{2} }$

Answer 2

Answer:

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Step-by-step explanation:

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