Surface Area Unit Test
15 of 1615 of 16 Items
Question
Olga is making presents for her teachers and needs to wrap them. She places the gifts in a right circular cylinder with a height of 12 inches and diameter of 6 inches. How much wrapping paper does she need for each gift she is going to wrap? Use 3.14 for π .(1 point)
inches2
To find the surface area of the cylinder, you need to calculate the lateral surface area (wrapping paper needed for the side) and the area of the two circular ends.
1. Lateral surface area:
The lateral surface area of a cylinder can be found using the formula:
Lateral Surface Area = 2πrh, where r is the radius and h is the height.
Given that the diameter is 6 inches, the radius (r) is half of the diameter:
r = 6 / 2 = 3 inches
h = 12 inches
Now, plug in the values:
Lateral Surface Area = 2 * 3.14 * 3 * 12 = 226.08 square inches
2. Area of the two circular ends:
The area of one circular end of a cylinder can be found using the formula:
Area of a circle = πr^2
Now, plug in the radius:
Area of one circular end = 3.14 * 3^2 = 28.26 square inches
Since we have two circular ends, the total area of the two ends is:
2 * 28.26 = 56.52 square inches
Adding the lateral surface area and the area of the two ends gives the total surface area:
Total Surface Area = Lateral Surface Area + Total Area of the two ends
Total Surface Area = 226.08 + 56.52 = 282.6 square inches
Therefore, Olga needs 282.6 square inches of wrapping paper for each gift she is going to wrap.
Surface Area Unit Test
16 of 1616 of 16 Items
Question
Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points)
To calculate the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces.
1. Area of the base:
Since the base of the pyramid is a square, you can find the area of the base by squaring the base length:
Area of base = base length * base length
Area of base = 12 * 12 = 144 square units
2. Area of the four triangular faces:
To find the area of a triangular face, you can use the formula for the area of a triangle:
Area of a triangle = 0.5 * base * height
Given that the slant height is 18 and the base length is 12, the height of the triangle can be found using the Pythagorean theorem:
height^2 + (base/2)^2 = slant height^2
height^2 + 6^2 = 18^2
height^2 + 36 = 324
height^2 = 288
height ≈ √288 ≈ 16.97
Now, calculate the area of each triangular face:
Area of one triangular face = 0.5 * 12 * 16.97 ≈ 101.82 square units
Since the pyramid has 4 triangular faces, the total area of the four faces is:
Total area of the 4 triangular faces = 4 * 101.82 ≈ 407.28 square units
3. Total surface area:
The total surface area of the pyramid is the sum of the base area and the total area of the four triangular faces:
Total surface area = Area of base + Total area of the 4 triangular faces
Total surface area = 144 + 407.28 = 551.28 square units
Therefore, the surface area of the square pyramid is approximately 551.28 square units.
shorter
To find the total surface area of the square pyramid, you need to calculate the area of the base and the four triangular faces.
1. Area of the base:
Since the base is a square, the area of the base is base length squared:
Area of base = 12 * 12 = 144 square units
2. Area of the four triangular faces:
Each triangular face has a base length of 12 and a height of approximately 16.97. Using the formula for the area of a triangle:
Area of one triangular face ≈ 0.5 * 12 * 16.97 ≈ 101.82 square units
Total area of the four triangular faces ≈ 4 * 101.82 ≈ 407.28 square units
3. Total surface area:
Add the area of the base and the total area of the four triangular faces to get the surface area of the square pyramid:
Total surface area ≈ Area of base + Total area of triangular faces
Total surface area ≈ 144 + 407.28 ≈ 551.28 square units
Therefore, the surface area of the square pyramid is approximately 551.28 square units.