Surface Area Word Problems

Show your work for each problem.

1.
A shoe box has the shape of which 3D figure?
1. a)Cone
2. b)Rectangular prism
3. c)Sphere
4. d)Cylinder
Answer: Rectangular prism
A shoe box has 6 flat rectangular faces, making it a rectangular prism. Cylinders have circular faces, spheres are round balls, and cones have a circular base with a point.
2.
A basketball is best represented by which 3D shape?
1. a)Pyramid
2. b)Cylinder
3. c)Cube
4. d)Sphere
Answer: Sphere
A basketball is perfectly round, making it a sphere. The surface area formula for a sphere is .
3.
A cube has edges of 5 cm. What is its surface area in cm²?
Answer: 150
For a cube: cm².
4.
A sphere has a diameter of 10 cm. What is its radius in cm?
Answer: 5
Radius cm.
5.
When buying paint for a project, if you calculate you need 8.3 cans, how many should you buy?
1. a)8.3 cans
2. b)10 cans
3. c)8 cans
4. d)9 cans
Answer: 9 cans
You must round UP to 9 cans. Rounding down to 8 would leave you short. You can't buy 8.3 cans - you must buy whole cans.
6.
A gift box is 20 cm long, 15 cm wide, and 10 cm tall. How much wrapping paper is needed to cover it?
Answer: 1300
1. What formula do you use for a rectangular prism? 2(lw + lh + wh)
2. Calculate (length × width) 300
3. Calculate (length × height) 200
4. Calculate (width × height) 150
5. Add the three products together 650
6. Multiply by 2 for the final surface area 1300
7.
A sphere has a radius of 7 cm. Using , what is the surface area? (Round to the nearest whole number)
Answer: 616
cm².
8.
A cylindrical can has a radius of 4 cm and a height of 12 cm. Find the surface area using . (Round to the nearest whole number)
Answer: 402
1. What is the area of the two circular bases? () 100.48
2. What is the lateral (curved) surface area? () 301.44
3. Add both parts for total surface area (round to nearest whole) 402
9.
A painter needs to paint a room that is 5 m long, 4 m wide, and 3 m tall. If she only paints the walls (not floor or ceiling), what is the surface area?
1. a)54 m²
2. b)74 m²
3. c)94 m²
4. d)40 m²
Answer: 54 m²
Walls only: m².
10.
A square pyramid has a base edge of 6 cm and a slant height of 5 cm. What is the total surface area?
Answer: 96
Base: cm². Perimeter: cm. Lateral: cm². Total: cm².
11.
A cone has a radius of 3 cm and a slant height of 5 cm. Using , find the surface area. (Round to nearest whole number)
Answer: 75
1. Calculate the base area () 28.26
2. Calculate the lateral area () 47.1
3. Add for total surface area (round to nearest whole) 75
12.
A warehouse needs to be painted. It is 20 m long, 15 m wide, and 8 m tall. If one can of paint covers 40 m², how many cans are needed to paint all walls and roof (not the floor)?
Answer: 22
1. Calculate the area of the two longer walls () 320
2. Calculate the area of the two shorter walls () 240
3. Calculate the area of the roof () 300
4. Add all areas together 860
5. Divide by coverage per can and round UP 22
13.
A water tank is a cylinder with radius 3 m and height 10 m. Only the lateral surface (curved part) needs to be painted. Using , how many square meters need painting? (Round to nearest whole number)
Answer: 188
Lateral area = m².
14.
A globe has a diameter of 30 cm. Fabric to cover it costs 2 euros per 100 cm². Using , how much will the fabric cost?
Answer: 56.52
1. What is the radius? 15
2. Calculate the surface area () 2826
3. How many 100 cm² units? 28.26
4. Calculate total cost (2 euros per unit) 56.52
15.
A tent is shaped like a square pyramid with base 4 m × 4 m and slant height 3 m. How much canvas is needed for just the sides (no floor)?
1. a)16 m²
2. b)48 m²
3. c)40 m²
4. d)24 m²
Answer: 24 m²
Perimeter = m. Lateral area = m².
16.
Convert 2.5 m² to cm². (Enter number only)
Answer: 25000
m² cm². So m² cm².