Question

A bowling-ball maker starts with an 8.5-inch-diameter resin sphere and drills 3 cylindrical finger holes in it. Each hole is 1 inch in diameter and 3.5 inches deep. Which is the best estimate of the volume of resin in the finished ball?

Answer 1

313.313inches³

Explanation:

A bowling ball is spherical in shape hence,

The Formula used to calculate the volume of sphere is

= 4/3 πr³

For the question, we were given diameter.

Diameter of the bowling ball = 8.5 inches

Radius = Diameter ÷ 2

Radius = 8.5 inches ÷ 2

Radius = 4.25 inches

Hence,

Volume of a Sphere =

4/3πr³

= 4/3 × π ÷ 4.25

= 321.55509806inches³

Approximately = 321.56inches³

From the question we can see that the bowling ball has 3 cylindrical holes in it

With a diameter of 1 inch and a depth of 3.5inches

Hence we find the volume of these holes

Volume of a cylinder = πr²h

Diameter = 1 inch,

Radius = Diameter /2 = 1/2 inches

Height(Depth) = 3.5 inches

Volume of the cylindrical holes = π ×(1/2) ² × 3.5

Volumes = 2.749inches³

Since we have 3 holes ,

Volumes of the 3 holes = 2.749inches³ × 3

= 8.247inches³

The Volume of the total Spherical bowling ball

= Volume of the total bowling ball without holes - Volume of the cylindrical holes on the bowling ball

= 321.56inches³ - 8.247inches³

= 313.313inches³

Hence, the best estimate of the volume of resin in the finished ball = 313.313inches³

Answer 2

313.3084 in3

Explanation:

To find the final volume of the finished ball, we need to find the volume of the whole sphere and then decrease it by the volume of the three holes.

The volume of the sphere is given by this formula:

V = (4/3)*pi*r^3

Where r is the radius. In our case, the radius is 8.5 / 2 = 4.25 in, so the volume is:

V1 = (4/3)*pi*4.25^3 = 321.5551 in3

The volume of each cilindrical hole can be calculated as:

V = pi*r^2*h

Where r is the radius and h is the height. We have that the radius is 1/2 = 0.5 inches and the height is 3.5 inches, so:

V2 = pi*0.5^2*3.5 = 2.7489 in3

So the final volume is:

V = V1 - 3*V2 = 321.5551 - 3*2.7489 = 313.3084 in3