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Answer:

Given :-

• The diameter of the base of a cone is 10.5 cm and its slant height is 10 cm.

To Find :-

• What is the curved surface area of a cone.

Solution :-

First, we have to find the radius of a cone :

Given :

• Diameter = 10.5 cm

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Radius =\: \dfrac{Diameter}{2}}}\\[/tex]

So, by putting the value we get,

[tex]\implies \sf Radius =\: \dfrac{10.5}{2}\\[/tex]

[tex]\implies \sf\bold{Radius =\: 5.25\: cm}\\[/tex]

Hence, the radius of a cone is 5.25 cm .

Now, we have to find the curved surface area of a cone :

Given :

• Radius = 5.25 cm
• Slant Height = 10 cm

According to the question by using the formula we get,

[tex]\implies \sf\boxed{\bold{Curved\: Surface\: Area_{(Cone)} =\: {\pi}rl}}\\[/tex]

where,

• π = Pie or 22/7
• r = Radius
• l = Slant Height

So, by putting those values we get,

[tex]\implies \sf Curved\: Surface\: Area_{(Cone)} =\: \dfrac{22}{7} \times 5.25 \times 10\\[/tex]

[tex]\implies \sf Curved\: Surface\: Area_{(Cone)} =\: \dfrac{22}{7} \times 52.5\\[/tex]

[tex]\implies \sf Curved\: Surface\: Area_{(Cone)} =\: \dfrac{1155}{7}\\[/tex]

[tex]\implies \sf\bold{\underline{Curved\: Surface\: Area_{(Cone)} =\: 165\: cm^2}}\\[/tex]

[tex]\therefore[/tex] The curved surface area of a cone is 165 cm² .

Answer:

165 cm

Step-by-step explanation:

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