The volume of a right circular cone of radius r and height h is given by V = 1 /3 πr^2 h. Suppose that the height decreases from 20cm to 19.95cm

Question 1

The volume of a right circular cone of radius r and height h is given by V = 1 /3 πr 2 h. Suppose that the height decreases from 20cm to 19.95cm and the radius increases from 4cm to 4.05cm. Compare the change in volume of the cone with the estimate given by the linear approximation.

Question 2

Write V(r, h) for the volume of the cone to emphasize that it is a function of both radius r and height h. The volume of the old cone is V(20, 4) = 1675.52cm3 and the volume of the new cone is V(19.95, 4.05) = 1687.99cm3 . The change of volume is thus

Therefore the approximate volume of the new cone is

l(19.95, 4.05) = 1675.52 − 167.55 · 0.05 + 418.88 · 0.05 = 1688.09 .

The approximate change of volume is thus

l(19.95, 4.05) − V(20, 4) = 12.57 .

kratos · Answer 1 · 2020-06-21T21:40:46+0000

Write V(r, h) for the volume of the cone to emphasize that it is a function of both radius r and height h. The volume of the old cone is V(20, 4) = 1675.52cm3 and the volume of the new cone is V(19.95, 4.05) = 1687.99cm3 . The change of volume is thus

Therefore the approximate volume of the new cone is

l(19.95, 4.05) = 1675.52 − 167.55 · 0.05 + 418.88 · 0.05 = 1688.09 .

The approximate change of volume is thus

l(19.95, 4.05) − V(20, 4) = 12.57 .

The volume of a right circular cone of radius r and height h is given by V = 1 /3 πr^2 h. Suppose that the height decreases from 20cm to 19.95cm

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The volume of a right circular cone of radius r and height h is given by V = 1 /3 πr^2 h. Suppose that the height decreases from 20cm to 19.95cm

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