Question

OUESTION--Diameter of the base of a cone is 0.5 cm and its slant height is 10 cm. find its curved surface area.

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Answer 1

Given:

• Diameter of the base of a cone is 0.5 cm and its slant height is 10 cm.

Explanation:

FORMULA

$\\ \circ {\boxed{\underline{\sf{ Curved \ Surface \ Area_{(Cone)} = πrl }}}}$

Now, We can find the curved surface area of cone using suitable values.

$\huge{ \circ }$ Radius of the cone :-

Diameter = 2(Radius)

D = 2r

0.5 = 2r

${\sf{r = \dfrac{0.5}{2} cm }}$

According to Question,

$\colon\implies{\sf{ πrl }} \\ \\ \\ \colon\implies{\sf{ \dfrac{ \cancel{22} }{7} \times \dfrac{0.5}{ \cancel{2} } \times 10 }} \\ \\ \\ \colon\implies{\sf{ \dfrac{11}{7} \times 5 }} \\ \\ \\ \colon\implies{\sf{ 1.5 \times 5 }} \\ \\ \\ \colon\implies{\boxed{\mathfrak\pink{ 7.5 \ cm^2 }}}$

Hence,

• The Curved surface area of cone is 7.5 cm²

Answer 2

Correct Question :-

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. find its curved surface area.

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Understanding The Concept:-

Question :- What is Right circular Cone ?

Answer :- Right circular cone :-

If a right angled triangle is revolved about one of the two sides forming a right angle keeping the other side fixed in position then the solid so obtained by segments is called right circular cone.

Question :- What is Slant height ?

Answer :- Slant Height :-

The length of the line segment joining the vertex to any point on a circular edge of the base is called the slant height of the cone.

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Solution :-

Given Information :-

$\sf {diameter = 10.5 \: cm}$

$\therefore \sf{radius \: (r) = \frac{10.5}{2} = 5.25 \: cm}$

$\sf{slant \: height \: (l) = 10 \: cm}$

Formula Used :-

$\boxed{ \sf{curved \: surface \: area \: of \: cone = (\pi \times r \times l)}}$

Putting the values given,

Putting the values given, We get,

$: \implies \sf{curved \: surface \: area \: of \: cone } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 5.25 \times 10$

$: \implies \sf{curved \: surface \: area = 165 \: {cm}^{2} }$

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Final Answer :-

The curved surface area of a cone = 165cm²

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