A sphere is to be designed with a radius of 72 in.Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. (Hint: The formula for the volume of a sphere is V left parenthesis r right parenthesis equals 4 over 3 straight pi r cubed.)A. 452.39 space i n cubedB. 16 comma 286.02 space i n cubedC. 32 comma 572.03 space i n cubedD. 65 comma 144.07 space i n cubed
Question
A sphere is to be designed with a radius of 72 in.Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. (Hint: The formula for the volume of a sphere is V left parenthesis r right parenthesis equals 4 over 3 straight pi r cubed.)A. 452.39 space i n cubedB. 16 comma 286.02 space i n cubedC. 32 comma 572.03 space i n cubedD. 65 comma 144.07 space i n cubed
Solution
The formula for the volume of a sphere is V(r) = 4/3πr³.
We can find the differential dV, which represents the error in the volume, by taking the derivative of the volume with respect to r (the radius), and then multiplying by the error in the radius (dr).
The derivative of V(r) = 4/3πr³ with respect to r is dV/dr = 4πr².
If the possible error in measuring the radius is 0.5 in (dr = 0.5 in), then the maximum error in the volume (dV) is given by:
dV = (dV/dr) * dr = 4πr² * dr = 4π(72 in)² * 0.5 in = 32,572.03 in³.
So, the maximum error when measuring the volume of the sphere is approximately 32,572.03 cubic inches.
Therefore, the correct answer is C. 32,572.03 in³.
Similar Questions
The radius of a sphere was measured to be 30 cm with a possible error of 0.5 cm.(a) Use differentials to estimate the maximum error in the calculated surface area.
The radius of a sphere was measured and found to be 18 cm with a possible error in measurement of at most 0.05 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.2.46πcm38.62πcm39.72πcm37.6πcm3
Calculate the volume of a sphere, both in terms of π and to the nearest tenth. Use 3.14 for n.d = 9 ft 121.5 π cubic feet 381.5 cubic feet 972 π cubic feet 3052.1 cubic feet 19π cubic feet 59.7 cubic feet 17π cubic feet 53.4 cubic feet
The radius, R, of a sphere is 6.6mm. Calculate the sphere's volume, V.Use the value 3.14 for π, and round your answer to the nearest tenth. (Do not round any intermediate computations.)=Vmm3
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.