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# A cone has a height of 14cm and a volume of 12cm 3 . Fine the radius of the circular base. (Take pi= 22 / 7 )

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A cone has a height of 14cm and a volume of 12cm3. Fine the radius of the circular base. (Take pi=22/7)

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thanks

Guest Sep 14, 2017
edited by Guest  Sep 14, 2017
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volume of cone  =  (1/3)(area of base)(height)

volume of cone  =  (1/3)  (pi)(radius2) (height)

Plug in the information from the problem.

12 cm3        =  (1/3)  (pi)(radius2) (14 cm)

Multiply both sides by  3 .

36 cm3        =  (pi)(radius2) (14 cm)

Divide both sides by  14 cm.

36/14 cm2      =  (pi)(radius2)

Divide both sides by  pi  .

36/(14pi) cm2   =  (radius2)

Take the positive square root of both sides.

$$\sqrt{\frac{36}{14\pi}}\,\text{ cm}\,=\,\text{radius} \\~\\ \text{radius} \,=\,\sqrt{\frac{36}{14\pi}}\,\text{ cm} \,\approx\,\sqrt{\frac{36}{14(\frac{22}7)}}\,\text{ cm}\,=\,\sqrt{\frac{36}{44}}\,\text{ cm}\,\approx\,0.905\,\text{ cm}$$

hectictar  Sep 14, 2017

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