Which solid has the greatest volume?
a)A right cylindrical cylinder with a radius of 4 inches; b)A cube with a side of length of 4 inches; or c) a sphere with a radius of 4 inches?
http://www.math.com/tables/geometry/volumes.htm
To determine which solid has the greatest volume, we need to compare the volumes of the three given solids: a right cylindrical cylinder, a cube, and a sphere.
a) A right cylindrical cylinder:
The volume of a right cylindrical cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is given as 4 inches. However, since the height is not provided, we cannot calculate the volume of the cylinder.
b) A cube:
The volume of a cube is given by the formula V = s^3, where s represents the length of the side of the cube. In this case, the side length is given as 4 inches. Thus, the volume of the cube is V = 4^3 = 64 cubic inches.
c) A sphere:
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, the radius is given as 4 inches. Therefore, the volume of the sphere is V = (4/3)π(4^3) = (4/3)π(64) = 268.08 cubic inches (rounded to two decimal places).
Comparing the volumes, we find that the sphere has the greatest volume of 268.08 cubic inches, followed by the cube with a volume of 64 cubic inches. Unfortunately, we cannot determine the volume of the cylindrical cylinder without the height information. Hence, the sphere is the solid with the greatest volume among the given options.