Question

$diameter \: of \: the \: base \: of \: a \: cone \: is \: 10.5cm \: and \: its \: salant height \: is \: 10cm.find \: its \: curved \: surface \: area$
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Answer 1

Answer:

this is the answer of your question

Answer 2

Question:

The diameter of base of a cone is 10.5 cm and its slant height is 10 cm. Find the curved surface area of the cone.

Answer:

The curved surface area of the cone is 165 cm².

Step-by-step-explanation:

We have given that,

$\bullet\sf\:Diameter\:(\:d\:)\:=\:10.5\:cm\\\\\\\bullet\sf\:Slant\:height\:(\:l\:)\:=\:10\:cm$

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

Now, we know that,

$\pink{\sf\:CSA_{cone}\:=\:\pi\:r\:l}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:CSA_{cone}\:=\:\dfrac{22}{7}\:\times\:\dfrac{d}{2}\:\times\:10\:\:\:-\:-\:[\:Radius\:is\:half\:the\:diameter\:]\\\\\\\implies\sf\:CSA_{cone}\:=\:\dfrac{22}{7}\:\times\:\dfrac{10.5}{\cancel2}\:\times\:\cancel{10}\\\\\\\implies\sf\:CSA_{cone}\:=\:\dfrac{22}{\cancel7}\:\times\:\cancel{10.5}\:\times\:5\\\\\\\implies\sf\:CSA_{cone}\:=\:22\:\times\:1.5\:\times\:5\\\\\\\implies\sf\:CSA_{cone}\:=\:33\:\times\:5\\\\\\\implies\boxed{\red{\sf\:CSA_{cone}\:=\:165\:cm^2}}$

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:

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