Quadratic Equations

Question

The volume of a cone with height, h (m), and radius r (m), is given by the formula v=1/3 πR^2h. What is the radius of a cone with volume 168cm^3 and height 9cm

Answer 1

V= (1/3)pi(r)^2h

168 = (1/3)pi(r^2)9 = 3pir^2

r^2 = 168/3pi

r = sqr(168/3pi) = about 4.2

Answer 2

Volume of cone V = ¹/₃ πR²h

For radius R, rearrange so ^3V / _πh = R² => R = √ ( ^3V / _πh )

then substitute given values so R = √ ( ³⁽¹⁶⁸⁾ / _π(9) ) = √ ( ⁵⁶ / _π ) = 4.222 (3 dp) cm

double check: what is volume of cone with height 9 and R = 4.222?

¹/₃ π(4.222)²(9) = 168