Volume and Area Calculations

In this video, Mr. Hul explains the mathematical concepts behind calculating the area of a shaded region, the volume of a shell, and the design of a brick planter. The lesson begins with an introduction to finding the area of a shaded region by subtracting the area of a smaller rectangle from a larger one. It then moves on to calculating the volume of a shell and its insulation, followed by determining the water capacity in liters. Finally, the video covers the design of a brick planter, including calculating the number of bricks needed and the cost of materials.

What is the formula used to find the area of a shaded region in a rectangle?

• Area of large rectangle times area of small rectangle

• Area of small rectangle minus area of large rectangle

• Area of large rectangle minus area of small rectangle

• Area of large rectangle plus area of small rectangle

In Example 1, what is the first step in calculating the volume of the outer box?

• Calculate the surface area

• Convert dimensions to meters

• Write the formula for volume

• Subtract the volume of the inner prism

How do you find the volume of the insulation in the insulated box?

• Multiply the volumes of the outer and inner prisms

• Subtract the volume of the inner prism from the outer prism

• Divide the volume of the outer prism by the inner prism

• Add the volumes of the outer and inner prisms

What is the volume of the inner prism in liters?

• 6885 liters

• 68.85 liters

• 688.5 liters

• 6.885 liters

What shape is the brick planter designed in Exercise 1?

• Cylinder

• Sphere

• Right rectangular prism

• Cube

How do you calculate the interior dimensions of the planter?

• Subtract the thickness of the bricks from the exterior dimensions

• Add the thickness of the bricks to the exterior dimensions

• Multiply the thickness of the bricks by the exterior dimensions

• Divide the exterior dimensions by the thickness of the bricks

What is the volume of the bricks needed for the planter?

• 200 cubic feet

• 50 cubic feet

• 100 cubic feet

• 150 cubic feet

How many bricks are needed to construct the planter?

• 1371 bricks

• 258 bricks

• 500 bricks

• 1000 bricks

What is the cost of each brick used in the planter project?

• $1.00

• $1.50

• $0.50

• $0.82

How much does the school pay for the delivery of bricks?

• $45

• $60

• $30

• $15