# Find the Value of (1/h²)+(1/r²) :

The numerical value of the volume and the area of the lateral surface of a right circular cone are equal If the height of the cone be h and radius be r, the value of (1/h²)+(1/r²) is

- 3/1
- 1/3
- 1/9
- 9/1

**Answer is (3): 1/9**

**Explanation:-**According to the question,

pai r

^{2}h/3 = pai r (h

^{2}+ r

^{2})

^{1/2}

r h/3 = (h

^{2}+ r

^{2})

^{1/2}

Square on both side,

r^{2}h^{2}/9 = h^{2} + r^{2}

1/9 = (h^{2} + r^{2})/r^{2}h^{2}

1/ 9 = h^{2}/r^{2}h^{2} + r^{2}/h^{2}r^{2}

1/9 = 1/r^{2} + 1/h^{2}

Then, the value of (1/r^{2}) + (1/h^{2}) is 1/9

Hence, the answer is (3) 1/9.