Suppose you have 2 pieces of ice with the same volume but in different shapes. If one of the pieces has a greater surface area than the other, it will cool a beverage faster than will the ice with less surface area.

1. Describe 2 different pieces of ice that have the same volume, but have different surface areas.
2. Which piece of ice will cool a beverage faster?

Suppose this two-dimensional figure is rotated 360 degrees around the vertical axis shown. Each small square on the grid represents 1 square inch. What is the volume of the three‑dimensional figure?

A grid. A vertical line is drawn 5 units to the right. A four sided figure is shaded with points at 5 units right, 3 units up. Another point at 5 units right and 8 units up. Another point at 7 units right and 8 units up. Another point at 8 units right and 6 units up.

Technology required. A triangular prism has height 8 units. The base of the prism is shown in the image. What is the volume of the prism? Round your answer to the nearest tenth.

A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. It has a radius of 12 inches and a height of 8 inches. The cone starts filling up with water. What fraction of the volume of the cone is filled when the water reaches a height of 2 inches?

Find the volume of a pyramid whose base is a square with sides of length 4 units and that has a height of 10 units.

A solid has volume 4 cubic units and surface area 10 square units. The solid is dilated, and the image has volume 108 cubic units. What is the surface area of the image?