Question

A cone of height 8 m has a curved surface area 188.4 square metres.
Find its volume. (Take value of pie = 3.14.)​

Answer 1

Answer:

height of cone, h=8m

CSA of cone = 188.4 metre sq.

πrl=188.4 m^2

l=188.4/3.14 r

l= 60/ r

we know that,

${r}^{2} = {l}^{2} - {h }^{2}$

r^2=(60/r)^2 -8^2

r^2 =3600/r^2 -64

r^4 + 64r^2 -3600=0

Let r^2 =R to Simplify the equation a little

R^2 + 64R -3600=0

Solving this ,we get;

R=36

therefore... r=6

Now, Volume of a cone :

${\pi {r}^{2} h} \div 3$

=(3.14 *6*6*8)/3

=301.44 m^3

Step-by-step explanation:

$volume \: of \: cone \: =301.44 \: {m}^{3}$

Hope you get dear....

plz mark it as brainliest,if you find it helpful ...

Answer 2

Solution:

Given:

• Height of the cone = 8 m
• Curved surface area of cone = 188.4 sq. m

To Find:

• Volume of cone.

Formula used:

• $\sf{Slant\;Height\;(l)=\sqrt{(Height)^{2}+(Radius)^{2}}}$

• $\sf{Volume\;of\;cone=\dfrac{1}{3}\pi r^{2}h}$

Let radius of cone be "r" and slant height be 'l'.

⇒ Curved surface area of cone = 188.4 sq. m

⇒ πrl = 188.4

We know that, $\sf{Slant\;Height\;(l)=\sqrt{(Height)^{2}+(Radius)^{2}}}$

$\sf{\implies \pi r\big(\sqrt{r^{2}+h^{2}}\big)=188.4}$

$\sf{\implies 3.14\times r\sqrt{r^{2}+8^{2}}=188.4}$

$\sf{\implies r\sqrt{r^{2}+8^{2}}=60}$

Now, squaring both the sides, we get

$\sf{\implies r^{2}(r^{2}+8^{2})=60^{2}}$

$\sf{\implies r^{4}+64r^{2}=3600}$

$\sf{\implies r^{4}+64r^{2}-3600=0}$

Now, by using splitting middle term method we solve this equation,

$\sf{\implies r^{4}+64r^{2}-3600=0}$

$\sf{\implies r^{4}+100r^{2}-36r^{2}-3600=0}$

$\sf{\implies r^{2}(r^{2}+100)-36(r^{2}+100)=0}$

$\sf{\implies (r^{2}-36)(r^{2}+100)=0}$

$\sf{\implies r^{2}=36\;,-100}$

As we know radius cannot be negative.

$\sf{\implies r^{2}=36}$

$\sf{\implies r=6\;m}$

∴ Radius of cone = 6 m

$\sf{Now,\;volume\;of\;cone=\dfrac{1}{3}\pi r^{2}h}$

$\sf{\implies Volume=\dfrac{1}{3}\times 3.14\times 6\times 6\times 8}$

$\sf{\implies Volume=3.14\times 2\times 6\times 8}$

$\sf{\implies Volume=301.44\;m^{3}}$

Hence,

• Volume of cone = 301.44 m³