Question

A cone has a slant length of 10 and a diameter of 8. Height is unknown.

Answer 1

Answer: 153.56

Step-by-step explanation:

Hi, to answer this question we have to apply the next formulas:

Volume of a cone: 1/3 π r² h

Where r is the radius and h is the height (unknown)

Diameter = r x 2

8 = 2r

8/2 =r

r = 4  

Before calculating the volume we have to apply the Pythagorean Theorem to find h. (where the slant is the hypotenuse and h and r are the sides of the triangle)

10 ² = h² + 4²

Solving for h

100 = h² + 16

100-16 = h²

84= h²  

√84 =h

9.16= h

Back on the volume formula:

V= 1/3 π r² h

V =1/3 π 4² (9.16) =153.56