Respuesta :
Answer:
313.3084 in3
Step-by-step 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
Answer:
313.313inches³
Step-by-step 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
