Question

If a cone of height 8 m has a curved surface area of 188.4m^3 then find the radius of its base

Answer 1

$curved \: \: surface \: \: area \\ \pi \times r \times \sqrt{ {r}^{2} + {h}^{2} } = 188.4 \\ r \times \sqrt{ {r}^{2} + {8}^{2} } = \frac{188.4}{\pi} = 60 \\ {r}^{2} ( {r}^{2} + 64) = {60}^{2} = 3600 \\ {r}^{4} + 64 {r}^{2} - 3600 = 0 \\ ( {r}^{2} + 100)( {r}^{2} - 36) = 0 \\ {r}^{2} = - 100 \: \: or \: \: 36 \\ - ve \: \: value \: \: is \: \: not \: \: admissible \\ {r}^{2} = 36 \\ radius \: \: r = 6 \: m$

Answer 2

Answer:

CSA of a cone = πSR = 188.4 m^2

S = 188.4/(3.14xR) = 60/R

R2 = (S2-h2)

R2 = (60/R)2- 82

R4 + 64R2 - 3600 = 0

r2 + 64r - 3600 = 0         ... where r = R2

r = [-64±(4096+4x3600)]/2

= [-64±136]/2

Hence r = 36, and R = 6 m.

Step-by-step explanation: