Answered

A non-scale model of the earth has a diameter of 18 in. Within an outer clay layer, there is a core made of a ball with a diameter of 3 in.


What is the volume of the clay?

Use 3.14 to approximate pi and express your answer in hundredths.


in3

Verified Answer :

sonerika101

Ok so the formula for the volume of a sphere is \(\frac{4}{3} \pi r^{3}\)
r is the radius, which is half the diameter. Since the diameter of the whole sphere is 18 the radius would be half of that, which is 9. If you plug 9 into the formula you get 3052.08in.cubed. Now you must find the volume of the smaller core, the diameter of the core is 3, so the radius is 1.5 and if you plug that into the formula you get 14.13in.cubed. Since you're finding only the volume of the outside layer, you would subtract the volume of the core from the whole sphere, so 3052.08-14.13=3037.95
Your answer is 3037.95in.cubed

benlovespi

Using 3.14 as an estimate for pi, the answer is 3037.95 in. cubed. But if more digits of pi were used, the answer is 3039.49 in. cubed. I found the answer by using the sphere volume formula (4/3\(\pi\)\(r^{3}\)) on both sphere measurements, then subtracted the smaller core sphere from the rest of the sphere. The above named numbers were the result.

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