Question

The volume of the right circular cone is 9856 cm³. The diameter of the cone is 28 cm. Find the height, slant height and area of the lateral surface of the cone.

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Answer 1

GIVEN,

volume of right circular cylinder=9856cm^3

diameter of base=28cm.

then, radius=d/2=14cm

TO FIND,

height

slant hight(l)

lateral surface area

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SOLUTION,

volume of right circular cone =1/3πr^2h

9856cm^3=1/3πr^2h

9856cm^3=1/3*22/7*14*14*h

9856cm^3=616/3*h

9856cm^3*3/616=h

h=48cm.

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Now refer to the attachment

hence, slant height ( l)=50cm

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lateral lateral surface area of right circular cone=πrl

=22/7*14*50

=2200cm^2

Answer 2

❥${\red{\underline{\huge{\mathbb{Given:-}}}}}$

Volume of the cone=9856 cm³.

Diameter of the cone= 28 cm.

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❥${\red{\underline{\huge{\mathbb{To\:find:-}}}}}$

• Height of the cone.
• Slant height of the cone.
• Area of the lateral surface.

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❥${\red{\underline{\huge{\mathbb{Solution:-}}}}}$

Volume of the cone=9856 cm³.

Diameter= 28 cm.

★Radius= Diameter/2

So,

Radius =28/2 =14cm.

★

$volume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h$

According to the question,

$\frac{1}{3} \pi {r}^{2} h = 9856 \\ = > \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h = 9856 \\ > h = 9856 \times 3 \times \frac{7}{22} \times \frac{1}{14} \times \frac{1}{14} \\ = > h = 48$

• Height of the cone=48 cm.

Consider the slant height of the cone=l cm.

$l = \sqrt{ {r}^{2} + {h}^{2} } \\ \: \: \: = \sqrt{ {14}^{2} + {48}^{2} } \\ \: \: \: = \sqrt{2500} \\ \: \: \: = 50$

• Slant height of the cone= 50 cm.

★

$area \: of \: lateral \: surface = \pi \: r \: l$

Area of the lateral surface= (22/7×14×50 )cm²

=2200 cm²

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❥${\red{\underline{\huge{\mathbb{Answer:-}}}}}$

•Height of the cone is 48 cm.

•Slant height of the cone is 50 cm.

•Area of the lateral surface of the cone is 2200 cm².

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