A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
Which equation gives the volume of the sphere?
V = two-thirds (27 pi)
V = four-thirds (27)
V = two-thirds (27)
V = four-third (27 pi)
The correct equation to give the volume of the sphere is:
V = four-thirds (27 pi)
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.
Her work is shown below.
V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed.
What is Amie’s error?
Amie should have multiplied 54 by Two-thirds.
Amie should have multiplied 54 by Four-thirds pi.
Amie should have multiplied 54 by Four-thirds.
Amie should have multiplied 54 by Two-thirds pi.
Amie's error is that she should have multiplied 54 by four-thirds pi, not two-thirds.
Kayla says that the point labeled C in the diagram below is the center. Raymond says that point C is the radius.
A sphere. The center is C.
Who is correct and why?
Kayla is correct; the center is a fixed point in the middle of the sphere.
Kayla is correct; the center is a line segment from the center to the surface of the sphere.
Raymond is correct; the radius is the fixed point in the middle of the sphere.
Raymond is correct; the radius is a chord that is from the center to the surface of the sphere.
Kayla is correct. The center of a sphere is a fixed point in the middle of the sphere. The radius, on the other hand, is a line segment from the center to any point on the surface of the sphere. Thus, point C in the diagram is the center of the sphere, not the radius.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.
Her work is shown below.
V = four-thirds (8) cubed. V = four-thirds (512). V = StartFraction 2,048 Over 3 EndFraction meters cubed.
What is Yolanda’s error?
Yolanda should have found the volume by multiplying 8 by Two-thirds.
Yolanda should have found the volume by multiplying 8 by Four-thirds.
Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.
Yolanda should have found the volume with the formula V = two-thirds (8) cubed.
Yolanda's error is that she should have found the volume by multiplying 8 by four-thirds, not two-thirds.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
What is the volume of the sphere?
12 centimeters cubed
24 centimeters cubed
36 centimeters cubed
54 centimeters cubed
To find the volume of the sphere, we need to use the formula:
V = four-thirds pi r^3
Since the sphere and cylinder have the same radius and height, the volume of the cylinder is equal to the volume of the sphere. Given that the volume of the cylinder is 18 cubic centimeters, we can set up the equation:
18 = four-thirds pi r^3
To find the volume of the sphere, we can solve for r and substitute it into the volume formula. However, without knowing the value of pi, it is not possible to determine the exact volume. Therefore, none of the given options (12 cm^3, 24 cm^3, 36 cm^3, 54 cm^3) can be confirmed as the correct volume without additional information.
To find the volume of a sphere, you can use the formula: V = (4/3)πr³, where V represents the volume and r represents the radius of the sphere.
In the given problem, both the sphere and the cylinder have the same radius and height. The volume of the cylinder is given as 27π cubic feet.
Since the radius and height are the same for both shapes, the radius of the sphere is also equal to the radius of the cylinder.
Now, we can use the equation for the volume of the cylinder to find the radius of the sphere. Substituting the given volume of the cylinder (27π) into the formula and solving for r, we get:
27π = πr²h
27 = r²h
Since the height (h) is the same for both shapes, we can divide both sides of the equation by h to get:
27/h = r²
Now, we have the value of r² in terms of h, which represents the radius of the sphere.
To find the volume of the sphere, we can substitute the formula for the volume of a sphere (V = (4/3)πr³) and the value of r² into the equation:
V = (4/3)πr³
V = (4/3)π(27/h)³
V = (4/3)π(27³/h³)
V = (4/3)π(19683/h³)
V = 83578π/h³
Therefore, the equation that gives the volume of the sphere is V = 83578π/h³.