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?

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

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

the correct answer to your question is a. 4^4

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step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights