A nón lá is a traditional Vietnamese hat in the shape of a perfect cone. What is the surface area of a hat with a diameter of 38 cm and a slant height of 30 cm? Use 3.14 for pi.(1 point)
Responses
2,923.34 square centimeters
2,923.34 square centimeters
1,789.8 square centimeters
1,789.8 square centimeters
3,579.6 square centimeters
3,579.6 square centimeters
8,113.76 square centimeters
To calculate the surface area of the hat, we first need to find the radius of the base of the cone. The diameter is given as 38 cm, so the radius is half of that: 38 cm / 2 = 19 cm.
Next, we can use the slant height and radius to find the lateral surface area of the cone by using the formula:
Lateral surface area = π * radius * slant height.
Plugging in the values:
Lateral surface area = 3.14 * 19 cm * 30 cm = 1,789.8 square centimeters.
Therefore, the surface area of the hat is 1,789.8 square centimeters.
The correct answer is:
1,789.8 square centimeters
I apologize for the incorrect response. Let's try another option.
The correct answer for the volume of the glass is 502.4 cubic centimeters.
To calculate the volume of one cone-shaped cup, we can use the formula:
Volume = (1/3) * π * radius^2 * height
First, let's find the volume of one cup:
Volume = (1/3) * 3.14 * 7 cm * 7 cm * 12 cm
Simplifying the equation:
Volume = 1.047 * 7 cm * 7 cm * 12 cm
Volume ≈ 615.44 cubic centimeters
Since a pack contains 12 cups, we can multiply the volume of one cup by 12 to find the total volume of water a pack of 12 cups will hold:
Total Volume = 615.44 cubic centimeters * 12 = 7,385.28 cubic centimeters
Therefore, a pack of 12 cups will hold approximately 7,385.28 cubic centimeters of water.
The correct answer is:
7,385.28 cubic centimeters.
To find the diameter of the exercise ball, we can use the formula for the surface area of a sphere:
Surface Area = 4 * π * radius^2
First, let's rearrange the formula to solve for the radius:
radius^2 = Surface Area / (4 * π)
radius^2 = 13266.5 cm2 / (4 * 3.14)
radius^2 = 1060.7 cm2
Taking the square root of both sides, we find:
radius ≈ √1060.7 cm2
radius ≈ 32.5 cm
Finally, the diameter of the exercise ball is twice the radius, so:
Diameter ≈ 2 * 32.5 cm
Diameter ≈ 65 cm
Therefore, the diameter of the exercise ball is approximately 65 cm.
The correct answer is:
65 cm.
To calculate the volume of a sphere, we can use the formula:
Volume = (4/3) * π * radius^3
First, let's find the radius of the sphere. The diameter is given as 3.5 ft, so the radius is half of that: 3.5 ft / 2 = 1.75 ft.
Next, we can plug in the values into the formula:
Volume = (4/3) * 3.14 * (1.75 ft)^3
Simplifying the equation:
Volume ≈ 4.1867 * 1.75 ft * 1.75 ft * 1.75 ft
Volume ≈ 22.439 ft³ (rounded to the nearest hundredth)
Therefore, the volume of the sphere with a diameter of 3.5 ft is approximately 22.44 ft³.
The correct answer is:
22.44 ft.³
Apologies for the incorrect response. Let's try another option.
The correct answer is:
2 cones = 1 sphere
The volume of a cone that shares the same radius and height as the cylinder can be calculated using the formula:
Volume of Cone = (1/3) * Volume of Cylinder
In this case, the volume of the cylinder is given as 60 cm³.
Volume of Cone = (1/3) * 60 cm³
Volume of Cone = 20 cm³
Therefore, the volume of the cone that shares the same radius and height as the cylinder is 20 cm³.
The correct answer is:
20 cm³.
A glass has a height of 10 centimeters and a width of 8 centimeters. What is the volume of the glass?(1 point)
Responses
502.4 cubic centimeters
502.4 cubic centimeters
2,009.6 cubic centimeters
2,009.6 cubic centimeters
1,256 cubic centimeters
1,256 cubic centimeters
628 cubic centimeters
To calculate the volume of the glass, we can use the formula for the volume of a rectangular prism:
Volume = length * width * height
Plugging in the values:
Volume = 8 cm * 10 cm * 1 cm = 80 cubic centimeters.
Therefore, the volume of the glass is 80 cubic centimeters.
The correct answer is:
80 cubic centimeters.