Volume and Surface Area Problems

The video tutorial covers solving various volume-related math problems. It begins with calculating the volume of a cylindrical block of wood sliced in half, followed by determining the volume of water a cylindrical container can hold. The tutorial then explains how to calculate the amount of wrapping paper needed for a rectangular box. It also includes a problem on determining the time required to fill a cylindrical water tank at a constant rate. Finally, the video demonstrates how to calculate the mass of a concrete staircase using its volume and density.

What is the volume of the top piece of a cylindrical block of wood if the block is sliced in half and the original diameter is 4 cm and height is 5 cm?

• 20π cm³

• 40π cm³

• 10π cm³

• 5π cm³

If a cylindrical container can fit three tennis balls each with a radius of 2 inches, what is the volume of water it can hold when emptied?

• 60π cubic inches

• 36π cubic inches

• 48π cubic inches

• 24π cubic inches

How much wrapping paper is needed to cover a rectangular box with a square base of area 25 square inches and a volume of 100 cubic inches?

• 100 square inches

• 130 square inches

• 150 square inches

• 180 square inches

A cylindrical water tank with a base radius of 4 feet and height of 6 feet can be filled in 3 hours. How long will it take to fill a tank with a base radius of 6 feet and height of 8 feet at the same rate?

• 12 hours

• 15 hours

• 9 hours

• 6 hours

What is the mass of a concrete staircase with a rectangular base of 5 meters by 6 meters, three steps each with a rise of 0.2 meters, and a concrete density of 130 kg/m³?

• 1560 kg

• 1300 kg

• 1800 kg

• 2000 kg