Question

The radius of a spherical ball is measured at r = 25 cm. Estimate the maximum error in the volume and surface area if r is accurate to within 0.6 cm. (Round your answers to three decimal places.)

Answer 1

Answer:

Volume = 2384.582 cm^3

Surface Area = 189.626 cm^2

Step-by-step explanation:

With the accuracy of r within 0.6 cm minimum & maximum values are 25-0.3 and 25+0.3 respectively.

Taking r = 25 cm

Volume = (4/3)*Pi*R3 = 65449.847

Surface Area = 4*Pi*R2 = 7853.982

The minimum possible values for Volume and surface area would be:

if r = 24.7 cm

Volume = (4/3)*Pi*R3 = 63121.814 cm^3

Surface Area = 4*Pi*R2 = 7666.617 cm^2

The maximum possible values for Volume and surface area would be:

if r = 25.3 cm

Volume = (4/3)*Pi*R3 = 67834.429 cm^3

Surface Area = 4*Pi*R2 = 8043.608 cm^2

Error from Minimum values:

Volume = 2328.033 cm^3

Surface Area = 187.365 cm^2

Error from Maximum values:

Volume = 2384.582 cm^3

Surface Area = 189.626 cm^2