Question

CALCULATE THE CURVED SURFACE AREA OF A CONE OF
DIAMETER 7CM AND SLANTING HEIGHT 10CM

Answer 1

Answer:

The curved surface area of cone is

$\boxed{\red{\sf\:CSA_{cone}\:=\:110\:cm^{2}}}$

Step-by-step-explanation:

We have given that,

$\sf\:Diameter\:of\:cone\:(\:d\:)\:=\:7\:cm\\\\\sf\:Slant\:height\:of\:cone\:(\:l\:)\:=\:10\:cm$

We have to find curved surface area of cone i. e. $\sf\:CSA_{cone}$

We know that,

$\sf\:CSA_{cone}\:=\:\pi\:r\:l\\\\\implies\sf\:CSA_{cone}\:=\:\pi\:\frac{d}{2}\:l\:\:\:[\:\because\:r\:=\:\frac{d}{2}\:]\\\\\implies\sf\:CSA_{cone}\:=\:\frac{\cancel{22}}{\cancel7}\:\times\:\frac{\cancel7}{\cancel2}\:\times\:10\\\\\implies\sf\:CSA_{cone}\:=\:11\:\times\:10\\\\\implies\boxed{\red{\sf\:CSA_{cone}\:=\:110\:cm^{2}}}$

Additional Information:

1. Cone:

Any three dimensional figure having two surfaces with base circular in shape is called as cone.

2. Examples of conical objects:

Conical tent, ice - cream cone, sharpened end of pencil, etc are some examples of conical objects.

3. Important formulae related to cone:

A cone having height $h$, slant height $l$ and radius $r$ has following formulae:

$\pink{\sf\:1.\:Area\:of\:base\:=\:\pi\:r^{2}}\\\\\pink{\sf\:2.\:l^{2}\:=\:r^{2}\:+\:h^{2}\:\:\:\:or\:\:\:l\:=\:\sqrt{r^{2}\:+\:h^{2}}}\\\\\pink{\sf\:3.\:Curved\:surface\:area\:=\:\pi\:r\:l} \\\\\pink{\sf\:4.\:Total\:surface\:area\:=\:\pi\:r\:(\:r\:+\:l\:)}\\\\\pink{\sf\:5.\:Volume\:=\:\frac{1}{3}\:\pi\:r^{2}\:h}$

Answer 2

✯✯ QUESTION ✯✯

CALCULATE THE CURVED SURFACE AREA OF A CONE OF DIAMETER 7CM AND SLANTING HEIGHT 10CM ..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Diameter\:of\:Cone=7cm}$

$\longmapsto\tt{Radius\:of\:Cone=\dfrac{7}{2}cm}$

$\longmapsto\tt{Slant\:height\:of\:Cone=10cm}$

➥Now ,

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\pink{\sf{C.S.A\:of\:Cone=\pi{rl}}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{\dfrac{22}{\cancel{7}}\times\dfrac{\cancel{7}}{\cancel{2}}\times{10}}$

$\longmapsto\tt{22\times{5}}$

$\longmapsto\tt{\large{\boxed{\bold{\bold{\green{\sf{{110cm}^{2}}}}}}}}$

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✔Formulas Related to Cone : -

• Total Surface Area of Cone = πrl(l+r)
• Volume of Cone = 1/3 πr²h
• Curved Surface Area of Cone = πrl

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