use the image described to answer the question.
An illustration shows a rectangle of unknown height with a circle of radius 3 feet attached to its top left and a circle of radius 3 feet attached to its bottom right.
if the surface area of the net diagram of the right circular cylinder is 395.64 feet^2, find the height of the net diagram. Use 3.14 for π.
__ feet
To find the surface area of the net diagram of the right circular cylinder, we need to include the surface area of the two circles and the rectangle.
The surface area of a circle is given by the formula A = πr^2, where r is the radius. For one circle, the area would be 3.14 * 3^2 = 28.26 feet^2. Since there are two circles, the total area for the circles is 2 * 28.26 = 56.52 feet^2.
The surface area of the rectangle is given by the formula A = l * w, where l is the length and w is the width. In this case, the length is the height of the net diagram and the width is 3 feet.
Let the height of the net diagram be h feet. The surface area of the rectangle would be h * 3 = 3h feet^2.
Adding the areas of the circles and the rectangle together, we have:
56.52 + 3h = 395.64
3h = 339.12
h = 113.04
Therefore, the height of the net diagram is 113.04 feet.
not right
Apologies for the mistake in my previous response. Let's correct the calculation:
The surface area of the net diagram of a right circular cylinder consists of the areas of the two circles (top and bottom) and the lateral surface area of the cylinder (the rectangle).
1. The surface area of each circle is A = πr^2 = 3.14 * 3^2 = 28.26 square feet. Since there are two circles, the total area from the circles is 2 * 28.26 = 56.52 square feet.
2. The lateral surface area of the cylinder (rectangle part of the net diagram) is given by the formula A = 2πrh, where r is the radius of the circle (3 feet) and h is the height of the cylinder/net diagram.
Given that the total surface area of the net diagram is 395.64 square feet, we have:
Total Area = 2 * 28.26 + 2 * 3.14 * 3 * h = 395.64
56.52 + 18.84h = 395.64
18.84h = 339.12
h = 18 feet
Therefore, the height of the net diagram of the right circular cylinder is 18 feet.
use the image described to answer the question.
An illustration shows a horizontal rectangle of height 18 yards with a circle of diameter 15 yards attached to its top left and a circle of diameter 15 yards attached to its bottom right.
calculate the surface area. use 3.14 π.
a. 1,201.05 yards^2
b. 623.25 yards^2
c. 600.53 yards^2
d. 3,108.6 yards^2
To find the surface area of the net diagram of the right circular cylinder, we need to calculate the areas of the two circles and the rectangle.
Given:
- The diameter of each circle is 15 yards, so the radius (r) of each circle is half of the diameter, which is 15 / 2 = 7.5 yards.
- The height (h) of the rectangle is 18 yards.
1. Area of each circle:
- A = πr^2
- A = 3.14 * (7.5)^2
- A = 3.14 * 56.25
- A = 176.625 square yards
Since there are two circles, the total area from the circles is:
2 * 176.625 = 353.25 square yards
2. Area of the rectangle:
- A = length * width
- A = height * width
- A = 18 * 15
- A = 270 square yards
Now, the total surface area of the net diagram is the sum of the areas of the two circles and the rectangle:
353.25 + 270 = 623.25 square yards
Therefore, the surface area of the net diagram is 623.25 yards^2.
So, the correct answer is:
b. 623.25 yards^2
use the image described to answer the question.
An illustration shows a horizontal rectangle of unknown height (in meters) with a circle of diameter 12 meters attached to its top left and a circle of diameter 12 meters attached to its bottom right.
if the surface area of the net diagram of the right circular cylinder is 715.92 meters^2, find the height. Use 3.14 for π.
13 meters
42 meters
16 metets
6.5 meters
To find the height of the rectangle in the net diagram, follow these steps:
Given:
- Diameter of each circle = 12 meters
- Radius (r) of each circle = diameter / 2 = 12 / 2 = 6 meters
- Surface area of the net diagram = 715.92 meters^2
1. Calculate the area of each circle:
- Area = πr^2 = 3.14 * 6^2 = 3.14 * 36 = 113.04 square meters
Since there are two circles, total area from circles = 2 * 113.04 = 226.08 square meters
2. Let the height of the rectangle be h meters.
- The width of the rectangle is the diameter of the circle = 12 meters
3. The lateral surface area of the cylinder (rectangle part of the net diagram) is:
- Area = height (h) * perimeter of the base circumferences (two circles)
- Area = h * (2πr + 2πr) = 2hπr = 2h * 3.14 * 6 = 37.68h square meters
4. The total surface area of the net diagram:
- Total Area = Area from circles + Area from the rectangle
- 715.92 = 226.08 + 37.68h
- 37.68h = 715.92 - 226.08
- 37.68h = 489.84
- h = 13 meters
Therefore, the height of the rectangle in the net diagram is 13 meters. Hence, the correct answer is 13 meters.
Aleksandr has a roll of paper that is in the shape of a right circular cylinder. It has a height of 28 cm and a diameter of 15.5 cm. Help Aleksandr solve for the surface area. Use 3.14 for π .
1,508.77
1,739.95
1,362.76
4,234.29
To find the surface area of the right circular cylinder, which includes the curved surface area and the areas of the two circular bases, use the following steps:
Given:
- Height (h) of the cylinder = 28 cm
- Diameter of the cylinder = 15.5 cm (which means the radius, r = diameter / 2 = 15.5 / 2 = 7.75 cm)
- π = 3.14
1. Calculate the lateral surface area (curved surface area) of the cylinder:
- Lateral Surface Area = 2πrh (where r is the radius and h is the height)
- Lateral Surface Area = 2 * 3.14 * 7.75 * 28
- Lateral Surface Area = 1726.6 cm^2
2. Calculate the area of each circular base:
- Area of one base = πr^2
- Area of one base = 3.14 * 7.75^2
- Area of one base = 3.14 * 60.0625
- Area of one base = 188.4875 cm^2
- Total area of both bases = 2 * 188.4875 = 376.975 cm^2
3. Add the lateral surface area and the areas of the two bases to find the total surface area of the cylinder:
- Total Surface Area = Lateral Surface Area + 2 * Area of one base
- Total Surface Area = 1726.6 + 376.975
- Total Surface Area = 2103.575 cm^2
Therefore, the surface area of the right circular cylinder is approximately 2103.575 cm^2, which is closest to 1,739.95 from the given options.