Question

If the height, slant height and radius of the given cone is an integer, what could be the ratio of the height of cone, to the base? radius of its

15:17

5:7

60:61​

Answer 1

5:7

is the answer

hope it helps you friend ✌

Answer 2

The Main Answer is:  None Of The Above

Given: height (h), radius (r), and slant height (l) are all integers

To Find: Ratio of height to radius or (h/r)

Solution:

• We know in a cone, the slant height (l) = $\sqrt{h^{2} + r^{2} }$
• For all these values to be integers, the only possible cases are where the three are a Pythagorean triplet.
• A Pythagorean triplet is one where 3 integers/ sides of a triangle follow the rule $a^{2} + b^{2} =c^{2}$,

        where a, b and c are sides of a triangle.

• So, the numerator and denominator when squared and added should produce a perfect square.

For 15:17-

15² + 17² = 225 + 289 = 514

Here, 514 is NOT a perfect square. ∴ This is not the correct answer.

For 5:7-

5² + 7² = 25 + 49 = 74

Here, 74 is NOT a perfect square. ∴This is not the correct answer.

For 60:61-

60² + 61² = 3600 + 3721 = 7321

Here, 7321 is NOT a perfect square. ∴This is not the correct answer.

Hence, the answer is NONE OF THE ABOVE.

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