Question

What is the volume of a small cone if:

Answer 1

Answer:

Volume of smaller cone =301.44

Step-by-step explanation:

First let angle of cone be$\alpha$.

then $sin(\alpha )$ = 3/5       (For bigger triangle)

Same cone angle is for smaller one because they are similar.

$cos(\alpha )$ = 4/5

Now for smaller cone radius be R

3/5 =R/Slant height

Slant height =5/3R

Lateral surface area =$\frac{1}{2}R^{2}\beta$  [R = slant height]  

Given lateral surface area =60$\pi$ =$\frac{1}{2}(\frac{5R}{3} )^{2} \beta$   ...................................1

$2\pi R=\frac{5R}{3}\beta$        ................................................2

$\beta=\frac{6\pi }{5}$

Put angle beta in equation 1 and find the value of R

R =6 cm

Height =$\frac{4R}{3}$

Thus volume =$\frac{1}{3}\pi6^{2}*8$

                     =301.44