The cone shown below has a slant height of 15 centimeters and a height of 12 centimeters. What is the radius of the cone.

The answer to your question is 9 cm

Step-by-step explanation:

Data

slant height = 15 cm

height = 12 cm

radius = ?

Process

To solve this problem, use the Pythagorean theorem. The slant height is the hypotenuse, the height is the long leg and the radius is the short leg.

             c² = a² + b²

           slant height² = height² + radius²

-Solve for radius

           radius² = slant height² - height²

-Substitution

           radius² = 15² - 12²

-Simplification

            radius² = 225 - 144

            radius² = 81

-Result

            radius = 9 cm

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.