Question

Walter bought 2,000 cubic millimeters of clay for his sculpture. Now that he has molded the cone and the sphere, he wants to use the rest for decorations. How much clay does he have left for decorations?

Answer 1

Explanation:

Let's first find the total volume of clay used for the cone and the sphere:

For the cone, we need the formula for the volume of a cone: Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.

Let's assume the cone has a radius of 5 millimeters and a height of 10 millimeters. Then, the volume of the cone is:

Vcone = (1/3)π(5^2)(10) = (1/3)π(250) = 83.33 cubic millimeters (rounded to two decimal places)

For the sphere, we need the formula for the volume of a sphere: Vsphere = (4/3)πr^3, where r is the radius.

Let's assume the sphere has a radius of 4 millimeters. Then, the volume of the sphere is:

Vsphere = (4/3)π(4^3) = (4/3)π(64) = 268.08 cubic millimeters (rounded to two decimal places)

The total volume of clay used for the cone and the sphere is:

Vcone + Vsphere = 83.33 + 268.08 = 351.41 cubic millimeters (rounded to two decimal places)

To find the amount of clay left for decorations, we can subtract this volume from the original amount of clay:

2000 - 351.41 = 1648.59 cubic millimeters (rounded to two decimal places)

Therefore, Walter has 1648.59 cubic millimeters of clay left for decorations.