A sphere has a surface area of 28.26 in2. Find the diameter in inches, of the sphere. Use PI
Question 2
What is the surface area, in square inches, of a sphere with radius 3.5 in.? Use Pi and round your answer to the nearest hundredth, if necessary.
Question 3
Whats is the volume of a sphere with a radius of 18 cm?
LAST QUESTION
What is the volume of a sphere with a diameter of 23 in.?
Round to the nearest tenth.
A 1807.5
B.1982.4
C.2103.6
D.2027.8
1. a = 4pi*r^2
28.26 = 4*3.14*r^2
r = 3/2, so diameter = 3
2. use above formula
3. v = 4/3 pi r^3 = 4/3 * 3.14 * 18^3 = 24416.64
4. use above formula. To estimate, 4/3 * pi is about 4. 4*11.5^3 = 6083. Hmmm. Nothing close. (?)
A = 4 pi r ^ 2
A = 28.26
28.26 = 4 pi r ^ 2
28.26 / ( 4 pi ) = r ^ 2
r ^ 2 = 28.26 / ( 4 * 3.14 )
r ^ 2 = 28.26 / 12.56 = 2.25
r = sqrt ( 2.25 ) = 1.5 in
Question 2
A = 4 pi r ^ 2
A = 4 * pi * 3.5 ^ 2
A = 4 * 3.14 * 12.25
A = 153.86 in ^ 2
Question 3
V = 4 * pi * r ^ 3 / 3
V = 4 * 3.14 * 18 ^ 3 / 3
V = 4 * 3.14 * 5832 / 3
V = 73249.92 / 3
V = 24416.64 in ^ 3
LAST QUESTION
V = 4 * pi * r ^ 3 / 3
V = 4 * 3.14 * 23 ^ 3 / 3
V = 4 * 3.14 * 12167 / 3
V = 152817.52 / 3
V = 50939.1733 in ^ 3
V = 50939.2 in ^ 3
rounded to the nearest tenth
What is the radius of a sphere that has a surface area of 12.56 ? Use 3.14 for .
Recall the formula .
What is the radius of a sphere that has a surface area of 12.56 es003-1.jpg? Use 3.14 for es003-2.jpg.
Recall the formula es003-3.jpg.
To answer these questions, we will use the formulas for surface area and volume of a sphere.
1. Surface area of a sphere:
The formula to calculate the surface area of a sphere is given by:
Surface Area = 4πr^2, where r is the radius of the sphere.
Given: Surface Area = 28.26 in^2
To find the radius of the sphere, we can rearrange the formula:
Surface Area = 4πr^2
28.26 = 4πr^2
Now, divide both sides of the equation by 4π:
28.26 / (4π) = r^2
Take the square root of both sides to find the radius:
sqrt(28.26 / (4π)) = r
Finally, calculate the diameter using the radius:
Diameter = 2r
2. To find the surface area of the sphere with radius 3.5 in., we use the formula:
Surface Area = 4πr^2
where r = 3.5 in.
3. To find the volume of the sphere with a radius of 18 cm, we use the formula:
Volume = (4/3)πr^3
where r = 18 cm.
4. To find the volume of the sphere with a diameter of 23 in., we need to first calculate the radius using the formula:
Radius = diameter / 2
Then we can use the volume formula:
Volume = (4/3)πr^3
where r = radius.
Now, let's solve each question step by step.
Question 1:
Given Surface Area = 28.26 in^2
Calculate the radius, r:
r = sqrt(28.26 / (4π))
Calculate the diameter: Diameter = 2r
Question 2:
Given radius = 3.5 in.
Calculate the surface area using the formula: Surface Area = 4πr^2
Question 3:
Given radius = 18 cm.
Calculate the volume using the formula: Volume = (4/3)πr^3
Question 4:
Given diameter = 23 in.
Calculate the radius: r = diameter / 2
Calculate the volume using the formula: Volume = (4/3)πr^3
Please note that for question 4, you also provided answer choices in the form of letters. To make it easier, I will provide the volume as a numerical value, and you can compare it to the answer choices.