Use the image to answer the question.
An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C . What is its surface area?
(1 point)
ft.2
Skip to navigation
To find the surface area of the letter C sculpture, we need to calculate the surface area of each individual face and then add them together.
1. Top and bottom faces:
- Surface area = length x width
- Surface area = 15ft x 10ft = 150 ft² each
- Total for top and bottom faces = 150 ft² + 150 ft² = 300 ft²
2. Front face:
- Surface area = height x width
- Surface area = 15ft x 1ft = 15 ft²
3. Side arms (2 arms):
- Surface area = height x depth
- Surface area = 4ft x 1ft = 4 ft² each
- Total for both arms = 4 ft² + 4 ft² = 8 ft²
4. Missing section on the right side:
- Surface area = height x width
- Surface area = 4ft x 7ft = 28 ft²
Adding all these together:
Total surface area = 300 ft² (top and bottom) + 15 ft² (front) + 8 ft² (side arms) - 28 ft² (missing section)
Total surface area = 325 ft²
Therefore, the surface area of the letter C sculpture is 325 ft².
Use the image to answer the question.
An illustration shows a horizontal rectangle of unknown height (in feet) with a circle of diameter 9 feet attached to its top left and a circle of diameter 9 feet attached to its bottom right.
The surface area of the net diagram of the right circular cylinder is 522.81 feet2. Find the height of the curved surface. Use 3.14 for π.
(1 point)
feet
Skip to navigation
To find the height of the curved surface of the right circular cylinder, we first need to calculate the surface area of the net diagram, which consists of the top circle, the bottom circle, and the curved surface.
1. Surface area of the top circle:
- Area = πr^2
- Diameter of the circle = 9 feet, so radius (r) = 9/2 = 4.5 feet
- Area = π(4.5)^2 = 3.14 x 20.25 = 63.585 ft²
2. Surface area of the bottom circle (same as the top circle):
- Area = 63.585 ft²
3. Surface area of the curved surface:
- The curved surface is a rectangle with a length equal to the circumference of the circles (2πr) and a height equal to the height of the cylinder (h).
- Circumference of the circles = 2πr = 2 x 3.14 x 4.5 = 28.26 feet
- The curved surface area = 2 x 28.26 x h = 56.52h ft²
Given that the total surface area of the net diagram is 522.81 ft², we can add up the areas we calculated:
63.585 ft² (top circle) + 63.585 ft² (bottom circle) + 56.52h ft² (curved surface) = 522.81 ft²
127.17 + 56.52h = 522.81
56.52h = 522.81 - 127.17
56.52h = 395.64
h = 395.64 / 56.52
h ≈ 7 feet
Therefore, the height of the curved surface of the right circular cylinder is approximately 7 feet.
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 calculate the amount of wrapping paper Olga needs for each gift, we need to find the surface area of the right circular cylinder.
1. Calculate the radius of the circular base:
- The diameter of the cylinder is 6 inches, so the radius (r) is half of that, which is 6/2 = 3 inches.
2. Calculate the surface area of the top and bottom circles:
- Area = πr^2
- Area = 3.14 x (3 inches)^2
- Area = 3.14 x 9
- Area = 28.26 square inches for each circle.
3. Calculate the surface area of the curved surface (wrapping paper needed):
- The curved surface area of a cylinder is 2πrh, where r is the radius and h is the height.
- Curved surface area = 2 x 3.14 x 3 inches x 12 inches
- Curved surface area = 75.36 square inches
To find the total wrapping paper needed, add the surface area of the top and bottom circles to the curved surface area:
28.26 square inches (top circle) + 28.26 square inches (bottom circle) + 75.36 square inches (curved surface)
Total wrapping paper needed = 131.88 square inches
Therefore, Olga needs 131.88 square inches of wrapping paper for each gift she is going to wrap.
that doesnt seem like the correct answer
Let's re-calculate the surface area of the right circular cylinder and determine the amount of wrapping paper needed for Olga's gifts.
Given:
- Height of the right circular cylinder (h) = 12 inches
- Diameter of the cylinder, which is the same as the length of the base circle = 6 inches
1. Calculate the radius (r) of the circular base:
Since the diameter is 6 inches, the radius is half of that:
r = 6 / 2 = 3 inches
2. Calculate the total surface area of the right circular cylinder:
- Surface area of the top and bottom circles = 2 * π * r^2
- Surface area of the top and bottom circles = 2 * 3.14 * 3^2
- Surface area of the top and bottom circles = 2 * 3.14 * 9
- Surface area of the top and bottom circles = 56.52 square inches
- Surface area of the curved surface (lateral surface area) = 2 * π * r * h
- Surface area of the curved surface = 2 * 3.14 * 3 * 12
- Surface area of the curved surface = 2 * 3.14 * 36
- Surface area of the curved surface = 226.08 square inches
3. Total surface area of the right circular cylinder:
Total surface area = Surface area of the top and bottom circles + Surface area of the curved surface
Total surface area = 56.52 + 226.08
Total surface area = 282.6 square inches
Therefore, Olga needs 282.6 square inches of wrapping paper for each gift she is going to wrap.