Question

CALCULATE THE TOTAL SURFACE AREA OF A CONE OF
RADIUS 21CM AND HEIGHT 10CM.

Answer 1

Radius =21 cm

Height=10 cm

Total surface area of cone=πr(l+r)

Now,

Slant height (l) =√r²+h²

l=√441+100

l=√541

l=23.25

Now substituting the values in formula,

TSA=22/7×21(23.25+21)

TSA=66(44.25)

TSA=2920.5 cm²

Answer 2

Answer:

Total surface area of the cone is

$\boxed{\red{\sf\:TSA_{cone}\:=\:2921.16\:cm^{2}}}$

Step-by-step-explanation:

We have given that, $\sf\:Radius\:of\:cone\:(\:r\:) \:=\:21\:cm\\\\\sf\:Height\:of\:cone\:(\:h\:)\:=\:10\:cm$

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

We know that,

$\sf\:TSA_{cone}\:=\:\pi\:r\:(\:r\:+\:l\:)$

We have to find first slant height of cone i. e. $\sf\:l\:$.

We know that,

$\sf\:l\:=\:\sqrt{r^{2}\:+\:h^{2}}\\\\\implies\sf\:l\:=\:\sqrt{21^{2}\:+\:10^{2}}\\\\\implies\sf\:l\:=\:\sqrt{441\:+\:100}\\\\\implies\sf\:l\:=\:\sqrt{541}\\\\\implies\sf\:l\:=\:23.259\\\\\implies\sf\:l\:\approx\:23.26$

Now,

$\sf\:TSA_{cone}\:=\:\pi\:r\:(\:r\:+\:l\:)\\\\\implies\sf\:TSA_{cone}\:=\:\frac{22}{\cancel7}\:\times\:\cancel{21}\:(\:21\:+\:23.26\:)\\\\\implies\sf\:22\:\times\:3\:(\:44.26\:)\\\\\implies\sf\:TSA_{cone}\:=\:66\:\times\:44.26\\\\\implies\boxed{\red{\sf\:TSA_{cone}\:=\:2921.16\:cm^{2}}}$

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:

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