Volume and Surface Area of Prisms

The video tutorial covers three challenging math problems. The first problem involves calculating the volume of a rectangular tank that is partially filled with water and determining how much more is needed to fill it completely. The second problem focuses on calculating the surface area of a cube and comparing it to a larger cube. The final problem involves finding the volume of a rectangular prism with a square base and a given height-to-width ratio.

What is the initial condition of the rectangular tank in the problem?

• It is one-third filled with water.

• It is half-filled with water.

• It is completely empty.

• It is completely filled with water.

How many cubic centimeters are needed to make the tank 6/10 full?

• 1300 cm³

• 1950 cm³

• 650 cm³

• 3900 cm³

What is the volume of one unit of additional water needed to fill the tank?

• 500 cm³

• 600 cm³

• 650 cm³

• 700 cm³

How many units of additional water are needed to make the tank 6/10 full?

• 7 units

• 6 units

• 5 units

• 4 units

What is the surface area of one face of the cube?

• 64 cm²

• 49 cm²

• 36 cm²

• 25 cm²

What is the total surface area of the original cube?

• 200 cm²

• 250 cm²

• 216 cm²

• 150 cm²

How many faces does a cube have?

• 6

• 8

• 4

• 5

If the edge of the cube is tripled, what is the new length of one edge?

• 18 cm

• 21 cm

• 12 cm

• 15 cm

What is the new surface area of the cube after scaling?

• 1296 cm²

• 1728 cm²

• 1944 cm²

• 2160 cm²

What is the difference in surface area after the cube is scaled?

• 1800 cm²

• 1500 cm²

• 1600 cm²

• 1728 cm²