Question

19 mark for review a right circular cone has a volume of 71,148π cubic centimeters and the area of its base is 5,929π square centimeters. what is the slant height, in centimeters, of this cone? a 12 b 36 c 77 d 85

Explanation:

Step1: Find the radius of the base

The area of the base of a cone is given by \( A = \pi r^2 \). We know \( A = 5929\pi \), so:

$$ \pi r^2 = 5929\pi $$

Divide both sides by \( \pi \):

$$ r^2 = 5929 $$

Take the square root: \( r = \sqrt{5929} = 77 \) cm.

Step2: Find the height of the cone

The volume of a cone is \( V = \frac{1}{3}\pi r^2 h \). We know \( V = 71148\pi \) and \( r = 77 \), so:

$$ 71148\pi = \frac{1}{3}\pi (77)^2 h $$

Divide both sides by \( \pi \):

$$ 71148 = \frac{1}{3}(5929)h $$

Multiply both sides by 3:

$$ 213444 = 5929h $$

Divide by 5929: \( h = \frac{213444}{5929} = 36 \) cm.

Step3: Find the slant height (\( l \))

Using the Pythagorean theorem for the cone (\( l = \sqrt{r^2 + h^2} \)):

$$ l = \sqrt{77^2 + 36^2} = \sqrt{5929 + 1296} = \sqrt{7225} = 85 $$

Answer:

D. 85