1 Answer | Add Yours
The surface area of a sphere with radius r is `(4/3)*pi*r^3` and the surface area of the sphere is `4*pi*r^2` .
Let the radius of the larger sphere be R, the surface area is `4*pi*R^2` , as the same material is used to create four smaller spheres with equal radius, the surface area of each of them is `pi*R^2` . This makes the radius of the sphere `sqrt((pi*R^2)/(4*pi)) = R/2 `
The volume of each sphere is `(4/3)*pi*(R/2)^3` . The total volume of all the four is `(16/3)*pi*R^3/8` = `(2/3)*pi*R^3`
As the volume of the large circle from which the four smaller ones are created is `(4/3)*pi*R^3` there is a decrease in the initial volume to half.
The volume of the smaller spheres is half of the volume of the larger sphere.
We’ve answered 318,955 questions. We can answer yours, too.Ask a question