Question

A cone and a sphere enclose a solid. What is the volume of this solid?

a) V = (1/3)πr²h + (4/3)πr³
b) V = (1/3)πr²h - (4/3)πr³
c) V = (4/3)πr³ - (1/3)πr²h
d) V = (4/3)πr³ + (1/3)πr²h

Answer 1

The volume of a solid that includes both a cone and a sphere is the sum of their individual volumes. The total volume is calculated with the formula
`V = (1/3)πr²h + (4/3)πr³`.

Step-by-step explanation:

When considering a solid comprising both a cone and a sphere, we must look at each shape individually to calculate the total volume. For a cone, the formula to find volume is
`V = (1/3)πr²h` where 'r' is the radius of the base of the cone and 'h' is the height of the cone. For a sphere, the volume is calculated using the formula , where 'r' is the radius of the sphere. To find the volume of a solid that includes both a cone and a sphere, you would smply add the individual volumes of both shapes.

If the question implies that the solid is made by enclosing a sphere with a cone (implying both share the same radius and the cone's tip is at the center of the sphere), then the total volume of the solid is the sum of the volumes of both shapes. Therefore, the correct formula for the total volume of the solid is
`V = (1/3)πr²h + (4/3)πr³` which corresponds to option (a).