A CONE HAS A BASE RADIUS OF 5CM AND HEIGHT OF 12 CM.CALCULATE ITS SLANT HEIGHT.

Draw a side view. It should be clear that the slant height s is

√(5^2 + 12^2) = 13

You can save yourself a lot of calculation if you just memorize a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples

To calculate the slant height of a cone, you can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In the case of a cone, the slant height is the hypotenuse, while the base radius and the height of the cone form the other two sides of the right-angled triangle.

In this case, we have the base radius (r) of 5 cm and the height (h) of 12 cm. We are trying to find the slant height (l).

The first step is to find the perpendicular height of the cone (also called the "altitude"), which can be done using the Pythagorean theorem:

h^2 = l^2 - r^2

Since we know the values for h and r, we can substitute them into the equation:

(12 cm)^2 = l^2 - (5 cm)^2
144 cm^2 = l^2 - 25 cm^2
l^2 = 169 cm^2

Now, take the square root of both sides to solve for l:

l = √169 cm^2
l = 13 cm

So, the slant height of the cone is 13 cm.

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