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 should have multiplied 54 by 2/3

Step-by-step explanation:

The formula of the volume of a sphere is given by

, where r is the radius of the sphere.

to find the volume of the sphere, we must find

We know that the formula of a cylinder of height h and radius r is given by

So

We know that the sphere and the cylinder have the same height. Recall that the height of the sphere of radius r, is the diameter of a circle that passes through the heighest and lowest points of the sphere. Then, h=2r. This means that

From here, we know that .

So the volume of the sphere is .

So Amie should have multiplied 54 by 2/3.

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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