Question

the curved surface area of a cone is 204.1 cm² and it's radius is 5 cm. what is its perpendicular height? (pie =3.14)

Answer 1

CSA of cone =πrl
πrl=204.1
l=204.1/3.14*5
l=204.1/15.7
l=13cm
h=√l square-r square
h=√13*13 - 5*5
h=√169-25
h√144
h=12cm

Answer 2

The perpendicular height is 12 cm.

Step-by-step explanation:

The curved surface area of a cone is

$A=\pi r(\sqrt{r^2+h^2})$

where, r is radius and h is height of the cone.

It is given that the curved surface area of a cone is 204.1 cm² and it's radius is 5 cm.

Substitute r=5, $\pi=3.14$ and A=204.1 in the above formula.

$A=\pi r(\sqrt{r^2+h^2})$

$204.1=(3.14)(5)(\sqrt{(5)^2+h^2})$

$204.1=15.7\sqrt{(5)^2+h^2}$

Divide both sides by 15.7.

$\frac{204.1}{15.7}=\sqrt{25+h^2}$

$13=\sqrt{25+h^2}$

Taking square on both sides.

$(13)^2=25+h^2$

$169=25+h^2$

Subtract 25 from both sides.

$169-25=h^2$

$144=h^2$

Taking square root on both sides.

$12=h$

Therefore, the perpendicular height is 12 cm.

#Learn more:

The radius of a cone is 7 cm and area of the curved surfaces is 176 cm². Find the slant height

https://brainly.in/question/1986123

Curved surface area of cone .

brainly.in/question/8861560