Find the Surface Area of the cylinder in terms of Pi. The cylinder is 14ft in height and 7 ft in radius.
686π
686 pi
294π
294 pi
784π
784 pi
714π
The formula to find the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height.
Given that the height is 14ft and the radius is 7ft, we can substitute these values into the formula:
Surface Area = 2π(7^2) + 2π(7)(14)
= 2π(49) + 2π(98)
= 98π + 196π
= 294π
Therefore, the surface area of the cylinder is 294π.
Find the surface area of the cone. Give your final answer rounded to the nearest whole number. Use 3.14 for pi. the cone is 14in height and the base is 11in.
The formula to find the surface area of a cone is πr(r + l), where r is the radius of the base and l is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem. The slant height, l, can be found as the hypotenuse of a right triangle formed by the height, h, and the radius, r:
l = √(r^2 + h^2)
l = √(11^2 + 14^2)
l = √(121 + 196)
l = √317
l ≈ 17.8
Now, we can substitute the values into the formula:
Surface Area ≈ 3.14 * 11(11 + 17.8)
Surface Area ≈ 3.14 * 11 * 28.8
Surface Area ≈ 968.03
Rounding to the nearest whole number, the surface area of the cone is 968.
The surface area of an exercise ball is 1256. Using 3.14 as the value of pi, what is the diameter of the exercise ball?(You know the surface area, pi, and 4. Undo the formula to find the radius and then diameter)
20
20
10
10
12
12
15
The formula for the surface area of a sphere is given by 4πr^2, where r is the radius of the sphere.
Given that the surface area of the exercise ball is 1256, we can set up the equation as follows:
1256 = 4πr^2
Simplifying the equation by dividing both sides by 4π:
r^2 = 1256 / (4π)
r^2 = 1256 / (4 * 3.14)
r^2 ≈ 100
Taking the square root of both sides to solve for r:
r ≈ √100
r ≈ 10
Finally, to find the diameter, we multiply the radius by 2:
d = 2 * r
d = 2 * 10
d = 20
Therefore, the diameter of the exercise ball is 20.
The volume of a cylinder is represented below
V=27π cm3
What would be the volume of a cone that has the same height and diameter as the cylinder?
(1 point)
Responses
V=18π cm3
V=18π cm3
V=3π cm3
V=3π cm3
V=9π cm3
V=9π cm3
V=81π cm3
The volume of a cylinder can be represented as V = πr^2h, where r is the radius of the base and h is the height.
Given that the volume of the cylinder is 27π cm^3, we can assume that the radius and height of the cylinder are the same. Therefore, the radius, r, and height, h, of the cylinder would be equal.
Let's assume r = h = x, where x is some value.
Substituting these values into the formula for the volume of a cylinder, we have:
27π = πx^2 * x
27 = x^3
Taking the cube root of both sides:
x = 3
Since r = x and h = x, the radius and height of the cylinder are both equal to 3.
Now, let's find the volume of a cone with the same height and diameter as the cylinder.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the radius and height of the cone are also 3, we can substitute these values into the formula:
V = (1/3)π(3^2)(3)
V = (1/3)π(9)(3)
V = (1/3)π(27)
V = 9π
Therefore, the volume of the cone with the same height and diameter as the cylinder is 9π cm^3.
The Crayola crayon shown below has a radius of 2mm. How much wax is needed to make the crayon? Use 3.14 for pi and round your answer to the nearest whole number.
To find the amount of wax needed to make the crayon, we need to calculate the volume of the crayon. The formula for the volume of a cylinder, which can be applied to the crayon, is V = πr^2h, where r is the radius and h is the height.
Given that the radius of the crayon is 2mm, we can assume the height of the crayon would be equal to or longer than the radius.
Substituting the values into the formula:
V = 3.14 * (2^2) * h
V = 3.14 * 4 * h
V = 12.56 * h
Since the question only asks for the amount of wax needed, we can round the volume to the nearest whole number.
Rounding 12.56 to the nearest whole number, we get 13.
Therefore, approximately 13 mm^3 of wax would be needed to make the crayon.
If the height of this cone is 20 yd and the volume is 3014.4 what is the radius?
Use 3.14 to solve and remember to show your work.