Question

the volume of a right circular cone is 1232 cm cube if the diameter of base is 14 cm then find the height of the cone slant height of the cone curved surface area of the cone

Answer 1

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Answer 2

Answer:

Slant height of the cone is 25 cm and curved surface area is 550 cm²

Step-by-step explanation:

Formula to get the volume of a circular cone is

$V=\frac{1}{3}\pi r^{2}h$

Here r = radius of the circular base of the cone

h = height of the cone

We can get the value of h when we plug in the values of r and V in the formula given in the question.

$1232=\frac{1}{3}\pi (\frac{14}{2})^{2}h$

$1232=\frac{1}{3}(\frac{22}{7})\times 49h$

$h=\frac{1232\times 21}{22\times 49}$

h = 24 cm

Now in the right angle triangle ABC,

l² = r² + h²[By Pythagoras theorem]

Where l² = 7² + 24²

$l=\sqrt{49+576}$

l = 25 cm

And curved surface area of the cone = $\pi rl$

                                                             = $(\frac{22}{7})(7)(25)$

                                                             = 550 square cm

Therefore, slant height (l) of the cone is 25 cm and the curved surface area is 550 square cm.

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