Use the image to answer the question.
An illustration shows a 3 D cuboid with length, width, and height marked as 5 centimeters. The edges that are not visible are marked as dashed lines.
Manny created a storage bin for the family to hold the remote control and cell phone cords. What is the total surface area of the storage bin?
The total surface area of a cuboid is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the length (l) = 5 cm, width (w) = 5 cm, and height (h) = 5 cm.
Plugging these values into the formula:
Surface Area = 2(5)(5) + 2(5)(5) + 2(5)(5)
Surface Area = 50 + 50 + 50
Surface Area = 150 square centimeters
Therefore, the total surface area of the storage bin is 150 square centimeters.
To find the surface area of the room that will be painted, we need to calculate the surface area of all six sides of the room (four walls, ceiling, and floor).
The formula for the surface area of a cuboid is:
Surface Area = 2lw + 2lh + 2wh
Given:
Length (l) = 20 ft
Width (w) = 15 ft
Height (h) = 9 ft
Plugging in these values:
Surface Area = 2(20)(15) + 2(20)(9) + 2(15)(9)
Surface Area = 600 + 360 + 270
Surface Area = 1230 square feet
Therefore, the surface area of the room that will be painted, including the floor and ceiling, is 1230 square feet.
To find the surface area of a triangular prism, we first need to calculate the surface area of each of the five faces (two triangular faces and three rectangular faces) and then add them up.
For a triangular face, the formula for the area is:
Area = 0.5 * base * height
For a rectangular face, the formula for the area is:
Area = length * height
Given:
- Height (h) = 9 inches
- Base of the triangle (b) = 17 inches
- Side 1 of the triangle (s1) = 10 inches
- Side 2 of the triangle (s2) = 12 inches
- Side 3 of the triangle (s3) = 17 inches
- Length of the prism (l) = 10 inches
Calculating the surface area of each face:
1. Surface area of the triangular face with sides s1, s2, and base b:
Area_triangular = 0.5 * b * h = 0.5 * 17 * 9 = 76.5 square inches
2. Surface area of the triangular face with sides s1, s3, and base b:
Area_triangular = 0.5 * b * h = 0.5 * 17 * 9 = 76.5 square inches
3. Surface area of the rectangular face on the bottom of the prism:
Area_rectangle = l * s1 = 10 * 10 = 100 square inches
4. Surface area of one of the rectangular faces making the sides of the prism:
Area_rectangle = l * s2 = 10 * 12 = 120 square inches
5. Surface area of the other rectangular face making the other sides of the prism:
Area_rectangle = l * s3 = 10 * 17 = 170 square inches
Adding up all the surface areas of the faces:
Total Surface Area = 76.5 + 76.5 + 100 + 120 + 170 = 543 square inches
Therefore, the surface area of the display showcase is 543 square inches.
To find the surface area of the triangular prism, we first calculate the surface area of all five faces (two triangular faces and three rectangular faces).
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Area of the triangular face + Perimeter of the triangle * length of the prism
Given:
- Base (b) of the triangle = 8 inches
- Perpendicular side of the triangle = 6 inches
- Hypotenuse of the triangle = 10 inches
- Length of the prism (l) = 19 inches
First, calculate the area of the triangle:
Area of the triangle = 0.5 * base * height = 0.5 * 8 * 6 = 24 square inches
Then, calculate the perimeter of the triangle:
Perimeter of the triangle = s1 + s2 + s3 = 8 + 6 + 10 = 24 inches
Now, we calculate the total surface area of the prism:
Surface Area = 2 * 24 + 24 * 19 = 48 + 456 = 504 square inches
Each pint of paint covers 200 square inches, so the number of pints needed will be:
Number of pints of paint = Surface Area / Coverage per pint = 504 / 200 = 2.52 pints
Since paint is sold in whole pints, the skateboard club will need to purchase 3 pints of paint to cover the entire model ramp.
For Monica’s 14th birthday, she wants to make over her bedroom. The first phase in the bedroom makeover is painting her room. If Monica’s room is 20 ft. long, 15 ft. wide, and 9 ft. high, find the surface area of the room that you are going to paint, including the floor and ceiling.
surface area = __ square feet
Christian collects model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h=9 inches, b=17 inches, s1=10 inches, s2=12 inches, s3= 17 and l=10 inches.
S.A.=__ in.2
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measure 19 inches and 8 inches. The perpendicular side of the triangular face measures 6 inches and the hypotenuse measures 10 inches.
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.
Number of pints of paint = __