Question

Find the radius of the cone if the ratio of it's volume to curved surface area is 16:9 and the ratio of it's slant heigjt and height is 9:8​

Answer 1

Answer:

Step-by-step explanation:

Let radius be 4x and height be 3x.

∴ Area of base = πr  

2

=154⇒  

7

22

​

×(4x)  

2

=154

⇒16x  

2

=  

22

154×7

​

⇒x  

2

=  

16

49

​

⇒x=  

4

7

​

 

∴ Radius = 4×  

4

7

​

=7cm,height=3×  

4

7

​

=  

4

21

​

=5.25cm

Now, CSA of cone = πrlandl=  

r  

2

+h  

2

 

​

=  

49+(5.25)  

2

 

​

 

∴ CSA =  

7

22

​

×7×8.75=192.5cm  

2