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The radius on a one is 3 cm and the surface area is 81pi squared. Find the slant height of this cone.
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18 votes
The radius on a one is 3 cm and the surface area is 81pi squared. Find the slant height of this cone.

User Seansand
by
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1 Answer

11 votes
11 votes

Answer

l = 24cm

Step-by-step explanation:

The radius of the cone = 3cm

Surface area = 81 pi squared cm

Surface area of the cone is given as


\text{Surface area = }\pi rl\text{ + }\pi\cdot r^2

l = h

r = 3cm


\begin{gathered} 81\pi\text{ = }\pi(rl+r^2) \\ 81\pi\text{ = }\pi(3\cdot l+3^2) \\ 81\pi\text{ = }\pi(3l\text{ + 9)} \\ \text{Divide both sides by }\pi \\ (81\pi)/(\pi)\text{ = }(\pi)/(\pi)(3l\text{ + 9)} \\ 81\text{ = 3l + 9} \\ \text{Collect the like terms} \\ 81\text{ - 9 = 3l} \\ 72\text{ = 3l} \\ \text{Divide both sides by 3} \\ l\text{ = }(72)/(3) \\ l\text{ = }24\operatorname{cm} \end{gathered}

Therefore, the slant height is 24cm

User Adam Peck
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