A chocolate is made in the shape of a sphere of diameter #4cm#, which has hollow inside of diameter #3.7cm#. What is the volume of the chocolate?
12.23 cu cm
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To find the volume of the chocolate, we first calculate the volume of the outer sphere and then subtract the volume of the hollow inside.
Volume of outer sphere ( = \frac{4}{3} \pi (\text{radius})^3 )
Volume of inner hollow ( = \frac{4}{3} \pi (\text{radius})^3 )
The difference gives us the volume of the chocolate.
Given the outer diameter is 4 cm, the radius of the outer sphere is ( \frac{4}{2} = 2 ) cm.
Given the inner diameter is 3.7 cm, the radius of the inner sphere is ( \frac{3.7}{2} = 1.85 ) cm.
Substituting these values into the formulas:
( \text{Volume of outer sphere} = \frac{4}{3} \pi (2)^3 = \frac{32}{3} \pi ) cubic cm
( \text{Volume of inner hollow} = \frac{4}{3} \pi (1.85)^3 \approx \frac{52.398}{3} \pi ) cubic cm
Therefore, the volume of the chocolate is the difference between these two volumes:
( \text{Volume of chocolate} = \left( \frac{32}{3} \pi \right) - \left( \frac{52.398}{3} \pi \right) ) cubic cm
( \text{Volume of chocolate} \approx \frac{32 - 52.398}{3} \pi ) cubic cm
( \text{Volume of chocolate} \approx -\frac{20.398}{3} \pi ) cubic cm
So, the volume of the chocolate is approximately ( -\frac{20.398}{3} \pi ) cubic cm.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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