Answer:
lateral surface area of the cone =49π
Step-by-step explanation:
y= x/4
dx/dy = 4
Given x range as from 0 ≤ x ≤ 7 ⇒ x ranges between (a,b)
a= x/4 = 0/4 = 0
b = x/4= 7/4
lateral surface area of the cone
[tex]\int\limits^b_a {2\pi x\sqrt{1 + (\frac{dx}{dy})^2 } } \, dx \\\\= \int\limits^{\frac{7}{4}}_0 {2\pi (4y)\sqrt{1 + (4)^2 } } \, dx \\\\= 32\pi \int\limits^{\frac{7}{4}}_0 { y } \, dx \\\\= 32\pi [\frac{y^2}{2}]|^\frac{7}{4}_0[/tex]
=32π * 49/(16 *2)
=49π
