Answer:
8 pieces of candy
Step-by-step explanation:
Take the original amount of candy in the bowl to be .
It says that 20 pieces of candy were added, therefore there are pieces of candy in the bowl.
Half of the candy is gone, therefore pieces of candy are left in the bowl.
After half of the candy is gone, there are 14 pieces left, so we can say that
Solve for :
Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
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For the complete question, refer to the attachment.
