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Multiple Choice Questions

391.

If f (x) = 3x² + 15x + 5, then find the approximate value of f (3.02) is

47.66
57.66
67.66
67.66

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Short Answer Type

392.

Find the approximate change in the volume V of a cube of side v meters caused by increasing the side by 2%.

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393.
Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

$straight V space equals space straight x cubed$
$Now space space space space space space space space space dV space equals space open parentheses dV over dx close parentheses increment straight x space equals space 3 straight x squared increment straight x space space space space space space space space space space space space space space space space space space space space space space equals space 3 straight x squared left parenthesis 0.01 space straight x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space 1 percent sign space of space straight x space is space 0.01 space straight x close square brackets$
$equals space 0.03 space straight x cubed straight m cubed$
$therefore space space space space approximate space change space in space volume space space equals space 0.03 space straight x cubed straight m cubed.$

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394. Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

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395.

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

118 Views

396.

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

93 Views

397.

If the radius of a sphere is measured as 9 m with an error of 0.03 m. then find the approximate error in calculating its surface area.

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398.

A circular disc of radius 3 cm is being heated. Due to expanison, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

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Multiple Choice Questions

399. The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

0.06 x³ m³
0.6 x³ m³
0.09 x³ m³
0.09 x³ m³

81 Views

Long Answer Type

400.

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, show that the area is maximum when the angle between them is 60°.

94 Views