From solid cylinder of h= 36cm and r=14cm, a conical cavity of radius 7cm and height 24cm is
drilled out. Find the volume and TSA of remaining solid. please explain
Solution
The volume of remaining solid is obtained subtracting the volume of the cone from the volume
of cylinder.
The voume of cylinder is:
V cyl. = [pi] *r^2*h
V cyl. = [pi] *14^2*36
V cyl. = 7056 [pi]
The voume of cone:
V cone = [pi] *r^2*h/3
V cone = [pi] *49*24/3
V cyl. = 392 [pi] cm^3
The volume of remaining solid is:
V = V cyl. - V cone
V = 6664 [ pi] cm^3
The total surface area of remaining solid is the TSA of cylinder + TSA of cone - 2*area of base
of cone:
TSA of cyl. = 2 [pi] r(r + h)
TSA of cyl. = 2 [pi ] *14(14+ 36)
TSA of cyl. = 1400 [pi] cm^2
TSA of cone = [pi] r(r+s)
We'll determine s using Pythagorean theorem:
s^2 = h^2 + r^2
s^2 = 24^2 + 7^2
s = sqrt(576+49)
s = 25
We'll consider only the positive value, since a length of a side cannot be negative.
TSA of cone = 7 [pi] (7+25)
TSA of cone = 224 [pi]
TSA of the remained solid is;
TSA of cyl. + TSA of cone = 1400 [pi] + 224 [pi] - 98 [pi] = 1526 [pi] cm^2
The volume and TSA of remainde solid are: V = 6664 [pi] cm^3 and TSA = 1526 [pi] cm^2.