Use the image to answer the question.
A cone is marked with a height of 15 centimeters and a diameter of 16 centimeters, both shown as perpendicular dotted lines. The slant height is 17 centimeters.
What is the height of the right circular cone?
(1 point)
17 cm
15 cm
16 cm
8 cm
15 cm
Use the image to answer the question.
An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.
Find the surface area of the cylinder below. Use the approximation 3.14 for pi.
(1 point)
Responses
533.8 square centimeters
1,099 square centimeters
628 square centimeters
628 centimeters
To find the surface area of the oblique cylinder, we first calculate the lateral surface area and add the areas of the two circles at the top and bottom.
1. Lateral Surface Area:
The lateral surface area of a cylinder is given by the formula: 2 * π * r * h, where r is the radius and h is the height.
Lateral Surface Area = 2 * 3.14 * 5 * 15
Lateral Surface Area = 471 square centimeters
2. Top and Bottom Circles:
The area of each circle is given by π * r².
Area of top circle = 3.14 * 5²
Area of top circle = 3.14 * 25
Area of top circle = 78.5 square centimeters
Area of bottom circle = 78.5 square centimeters
Now we add all the areas together:
Total Surface Area = Lateral Surface Area + 2 * Area of circle
Total Surface Area = 471 + 2 * 78.5
Total Surface Area = 471 + 157
Total Surface Area = 628 square centimeters
Therefore, the surface area of the oblique cylinder is approximately 628 square centimeters. So, the correct answer is:
628 square centimeters
Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet. Adrian wants to paint all around the outside of the cylinder, including the top and bottom faces. In order to understand how much paint is needed, he wants to know the surface are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? Use 3.14 for pi and round your answer to the nearest tenth.(1 point)
To find the surface area of the cylinder, we need to calculate the area of the top and bottom faces (circular areas) and the lateral surface area.
1. Area of the Top and Bottom Faces:
The area of a circle is given by A = π * r^2, where r is the radius.
Area of top and bottom faces = 2 * π * 4^2
Area of top and bottom faces = 2 * 3.14 * 16
Area of top and bottom faces = 100.48 square feet
2. Lateral Surface Area:
The lateral surface area of a cylinder is given by A = 2 * π * r * h, where r is the radius and h is the height.
Lateral Surface Area = 2 * 3.14 * 4 * 3
Lateral Surface Area = 75.36 square feet
Total Surface Area = Area of top and bottom faces + Lateral Surface Area
Total Surface Area = 100.48 + 75.36
Total Surface Area = 175.84 square feet
Therefore, the surface area of the outside of the cylinder is approximately 175.8 square feet.
Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi.(1 point)
square inches
To find the surface area of the cone peak, we need to calculate the lateral surface area.
First, we need to find the radius of the cone. Since the diameter is given as 14 inches, the radius (r) is half of the diameter:
r = 14 / 2 = 7 inches
Given that the slant height (l) is 20 inches, we can use the Pythagorean theorem to find the height (h) of the cone:
l^2 = r^2 + h^2
20^2 = 7^2 + h^2
400 = 49 + h^2
h^2 = 351
h = √351 ≈ 18.73 inches
Now, we can calculate the lateral surface area (A) of the cone using the formula:
A = π * r * l
A = 3.14 * 7 * 20
A = 439.6 square inches
Therefore, the surface area of the cone peak is approximately 439.6 square inches.
Use the image to answer the question.
A 3 D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.
Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.
(1 point)
cubic millimeters
To find the volume of the cylinder, we can use the formula for the volume of a cylinder which is given by V = π * r^2 * h, where r is the radius and h is the height.
Given:
- Base radius (r) = 8 mm
- Perpendicular height (h) = 13 mm
Substitute these values into the volume formula:
V = 3.14 * 8^2 * 13
V = 3.14 * 64 * 13
V ≈ 2649.92 cubic millimeters
Therefore, the volume of the cylinder is approximately 2649.92 cubic millimeters.