The volume of a sphere of radius r is V = 4/3 ? r³. (a) Write a differential formula that estimates the change in volume of a sphere when the radius changes from r? to r? + dr. Enter r? as r0 and dr as dr. dV = (b) Write a differential formula that estimates the change in volume of a sphere when the radius changes from 10 to 10 + dr. dV = (c) Use a differential to estimate the change in volume of a melting spherical snowball when the radius changes from 10 cm to 9.6 cm. dV = cm³
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The formula for the volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. Show more…
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(1 point) The volume of a sphere of radius r is V = 4/3 π r^3. (a) Write a differential formula that estimates the change in volume of a sphere when the radius changes from r0 to r0 + dr. Enter r0 as r0 and dr as dr. dV = (b) Write a differential formula that estimates the change in volume of a sphere when the radius changes from 12 to 12 + dr. dV = (c) Use a differential to estimate the change in volume of a melting spherical snowball when the radius changes from 12 cm to 11.5 cm. dV = cm^3
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Use the differential dV to estimate the change in volume of a sphere when the radius changes from 4 to 3.3. Round your answer to the nearest tenth, if necessary. Recall that the volume of a sphere is 4/3πr^3, where r is the radius of the sphere. Provide your answer below:
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