Question

1. kathleen’s ice cream cone has a diameter of 9 cm and a slant height of 7.5 cm. what is the height of the ice cream cone?

Explanation:

Step1: Find the cone's radius

Radius $r = \frac{\text{diameter}}{2} = \frac{9}{2} = 4.5$ cm

Step2: Apply Pythagorean theorem

The slant height $l$, height $h$, and radius $r$ form a right triangle: $h = \sqrt{l^2 - r^2}$
Substitute values: $h = \sqrt{(7.5)^2 - (4.5)^2}$

Step3: Calculate squared terms

$7.5^2 = 56.25$, $4.5^2 = 20.25$
$h = \sqrt{56.25 - 20.25}$

Step4: Compute final height

$h = \sqrt{36} = 6$ cm

Answer:

6 cm