SOLUTION: The altitude of a regular cone is twice its base radius. if its volume is 3,400 cubic meter what is the total surface area?

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Question 1138274: The altitude of a regular cone is twice its base radius. if its volume is 3,400 cubic meter what is the total surface area?
Answer by MathLover1(20850) About Me  (Show Source):
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The altitude of a regular cone is twice its base radius. if its volume is 3400 cubic meter what is the total surface area?

Since the base of a cone is a circle, the formula for finding the volume of a cone is:
V=%281%2F3%29pi%2Ar%5E2%2Ah
given:
the altitude of a regular cone is twice its base radius:h=2r
volume+is+V=3400
3400=%281%2F3%29pi%2Ar%5E2%2A2r
3400=%282pi%2F3%29r%5E3+
r%5E3=3400%2F%282%2F3%29pi
r%5E3=%283%2A3400%29%2F2pi
r%5E3=5100%2Fpi
r=root%283%2C5100%2Fpi%29
r=11.75

The total surface area of a cone is the sum of the area of its base and the lateral (side) surface.
the formula for the lateral surface area of a right cone is
L_S_A=+pi%2Ar%2Al , where l is the slant height of the cone
use r and h to find the slant height l
l=sqrt%28r%5E2%2Bh%5E2%29
l=sqrt%2811.75%5E2%2B%282%2A11.75%29%5E2%29
l=26.27
L_S_A=+pi%2A11.75%2A26.27
L_S_A=+969.72cm%5E2
area of the base:
B_A=r%5E2pi
B_A=11.75%5E2%2Api
B_A=433.74cm%5E2

=>The total surface area of a cone is:
A=B_A%2BL_S_A
A=433.74cm%5E2%2B969.72cm%5E2
A=1403.46cm%5E2