The lateral surface area and the area of the base of the cone are in the ratio 5:4. If the volume of the cone is 1024 pi m^{3, then find the height of the cone . Pls answer this early experts.}

Question

The lateral surface area and the area of the base of the cone are
in the ratio 5:4 If the volume of the cone is 1024 pi m3, then
find the height of the cone Pls answer this early experts
​​

Varun.Rawat · Accepted Answer

Let r be the radius of base, l be the slant height and h be the height of cone
Now, LSA = πrlArea of base = πr2⇒LSAArea of base = πrlπr2 = lr ⇒54 = lr⇒4l = 5r⇒l = 5r4Now, volume of cone = 13πr2h⇒1024π = 13πr2l2 - r2⇒1024 = r23 25r216 - r2 ⇒3072 = r29r216⇒3072 = r2 × 3r4⇒3r3 = 12288⇒r3 = 4096⇒r = 16Now, l = 5r4 = 5 × 164 = 20 mNow, h = l2 - r2 = 202 - 162 = 400 - 256 = 144⇒h = 12 m

The lateral surface area and the area of the base of the cone are in the ratio 5:4. If the volume of the cone is 1024 pi m3, then find the height of the cone . Pls answer this early experts. ​​

The lateral surface area and the area of the base of the cone are in the ratio 5:4. If the volume of the cone is 1024 pi m^{3, then find the height of the cone . Pls answer this early experts.}