Applications of Surface Area of Prisms Practice
The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to purchase? Paint is only sold in whole pints.
To find the surface area of the ramp, we need to calculate the total surface area of all the faces of the prism.
The ramp consists of 3 rectangular faces and 2 triangular faces.
Let's calculate the surface area of each face:
1. Rectangular faces (front and back):
Each rectangular face has a length of 10 feet and a width of 4 feet.
Area of one rectangular face = length x width
Area of one rectangular face = 10 ft x 4 ft
Area of one rectangular face = 40 square feet
There are 2 rectangular faces, so the total area of both rectangular faces = 40 sq ft x 2 = 80 sq ft
2. Bottom rectangular face:
The bottom rectangular face has a length of 12 feet and a width of 4 feet.
Area of the bottom rectangular face = length x width
Area of the bottom rectangular face = 12 ft x 4 ft
Area of the bottom rectangular face = 48 square feet
3. Triangular faces:
Each triangular face is a right triangle with a base of 10 feet and a height of 4 feet.
Area of one triangular face = 1/2 x base x height
Area of one triangular face = 1/2 x 10 ft x 4 ft
Area of one triangular face = 20 square feet
There are 2 triangular faces, so the total area of both triangular faces = 20 sq ft x 2 = 40 sq ft
Now let's calculate the total surface area of the ramp:
Total surface area = area of 2 rectangular faces + area of bottom rectangular face + area of 2 triangular faces
Total surface area = 80 sq ft + 48 sq ft + 40 sq ft
Total surface area = 168 square feet
Now, since 1 pint of paint covers 200 square inches, we need to convert the total surface area of the ramp from square feet to square inches:
1 square foot = 144 square inches
168 square feet = 168 sq ft x 144 sq in/sq ft = 24,192 square inches
Now let's calculate how many pints of paint the club will need to purchase:
Number of pints of paint = total surface area in square inches / coverage of 1 pint of paint
Number of pints of paint = 24,192 square inches / 200 square inches/pint
Number of pints of paint = 120.96
Since paint is only sold in whole pints, the club will need to purchase 121 pints of paint.