Rate of Change
Application of Derivatives

85128 If \(s=60 t-5 t^{2}\) denotes the distance covered by a particle in time ' \(t\) ', then the distance it covers before coming to rest is units.

1 120
2 720
3 240
4 180
Application of Derivatives

85129 A stone is dropped into a quiet lake and waves move in circles at the speed of \(6 \mathrm{~cm}\) per second. At the instant when the radius of the circular wave is \(12 \mathrm{~cm}\), the enclosed area is increasing at the rate of

1 \(120 \pi \mathrm{cm}^{2} / \mathrm{s}\)
2 \(130 \pi \mathrm{cm}^{2} / \mathrm{s}\)
3 \(144 \pi \mathrm{cm}^{2} / \mathrm{s}\)
4 none of these
Application of Derivatives

85130 The volume of a spherical ball is increasing at a rate of \(4 \pi \mathrm{cm}^{3} \mathrm{~s}^{-1}\). The rate at which its radius increases when its volume is \(288 \pi \mathrm{cm}^{3}\) is cm. \(\mathrm{s}^{-1}\)

1 \(1 / 6\)
2 \(1 / 36\)
3 \(1 / 9\)
4 \(1 / 24\)
[EAMCET 11.09.2020,Shift-II]
Application of Derivatives

85131 The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 \(\mathrm{cm}\) and \(20 \mathrm{~cm}\) respectively. If its diameter is increasing at a rate of \(2 \mathrm{~cm} / \mathrm{s}\), then at what rate must its altitude change in order to keep its volume constant?

1 \(4 \mathrm{~cm} / \mathrm{s}\)
2 \(6 \mathrm{~cm} / \mathrm{s}\)
3 \(-4 \mathrm{~cm} / \mathrm{s}\)
4 \(-8 \mathrm{~cm} / \mathrm{s}\)
Application of Derivatives

85128 If \(s=60 t-5 t^{2}\) denotes the distance covered by a particle in time ' \(t\) ', then the distance it covers before coming to rest is units.

1 120
2 720
3 240
4 180
Application of Derivatives

85129 A stone is dropped into a quiet lake and waves move in circles at the speed of \(6 \mathrm{~cm}\) per second. At the instant when the radius of the circular wave is \(12 \mathrm{~cm}\), the enclosed area is increasing at the rate of

1 \(120 \pi \mathrm{cm}^{2} / \mathrm{s}\)
2 \(130 \pi \mathrm{cm}^{2} / \mathrm{s}\)
3 \(144 \pi \mathrm{cm}^{2} / \mathrm{s}\)
4 none of these
Application of Derivatives

85130 The volume of a spherical ball is increasing at a rate of \(4 \pi \mathrm{cm}^{3} \mathrm{~s}^{-1}\). The rate at which its radius increases when its volume is \(288 \pi \mathrm{cm}^{3}\) is cm. \(\mathrm{s}^{-1}\)

1 \(1 / 6\)
2 \(1 / 36\)
3 \(1 / 9\)
4 \(1 / 24\)
[EAMCET 11.09.2020,Shift-II]
Application of Derivatives

85131 The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 \(\mathrm{cm}\) and \(20 \mathrm{~cm}\) respectively. If its diameter is increasing at a rate of \(2 \mathrm{~cm} / \mathrm{s}\), then at what rate must its altitude change in order to keep its volume constant?

1 \(4 \mathrm{~cm} / \mathrm{s}\)
2 \(6 \mathrm{~cm} / \mathrm{s}\)
3 \(-4 \mathrm{~cm} / \mathrm{s}\)
4 \(-8 \mathrm{~cm} / \mathrm{s}\)
Application of Derivatives

85128 If \(s=60 t-5 t^{2}\) denotes the distance covered by a particle in time ' \(t\) ', then the distance it covers before coming to rest is units.

1 120
2 720
3 240
4 180
Application of Derivatives

85129 A stone is dropped into a quiet lake and waves move in circles at the speed of \(6 \mathrm{~cm}\) per second. At the instant when the radius of the circular wave is \(12 \mathrm{~cm}\), the enclosed area is increasing at the rate of

1 \(120 \pi \mathrm{cm}^{2} / \mathrm{s}\)
2 \(130 \pi \mathrm{cm}^{2} / \mathrm{s}\)
3 \(144 \pi \mathrm{cm}^{2} / \mathrm{s}\)
4 none of these
Application of Derivatives

85130 The volume of a spherical ball is increasing at a rate of \(4 \pi \mathrm{cm}^{3} \mathrm{~s}^{-1}\). The rate at which its radius increases when its volume is \(288 \pi \mathrm{cm}^{3}\) is cm. \(\mathrm{s}^{-1}\)

1 \(1 / 6\)
2 \(1 / 36\)
3 \(1 / 9\)
4 \(1 / 24\)
[EAMCET 11.09.2020,Shift-II]
Application of Derivatives

85131 The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 \(\mathrm{cm}\) and \(20 \mathrm{~cm}\) respectively. If its diameter is increasing at a rate of \(2 \mathrm{~cm} / \mathrm{s}\), then at what rate must its altitude change in order to keep its volume constant?

1 \(4 \mathrm{~cm} / \mathrm{s}\)
2 \(6 \mathrm{~cm} / \mathrm{s}\)
3 \(-4 \mathrm{~cm} / \mathrm{s}\)
4 \(-8 \mathrm{~cm} / \mathrm{s}\)
Application of Derivatives

85128 If \(s=60 t-5 t^{2}\) denotes the distance covered by a particle in time ' \(t\) ', then the distance it covers before coming to rest is units.

1 120
2 720
3 240
4 180
Application of Derivatives

85129 A stone is dropped into a quiet lake and waves move in circles at the speed of \(6 \mathrm{~cm}\) per second. At the instant when the radius of the circular wave is \(12 \mathrm{~cm}\), the enclosed area is increasing at the rate of

1 \(120 \pi \mathrm{cm}^{2} / \mathrm{s}\)
2 \(130 \pi \mathrm{cm}^{2} / \mathrm{s}\)
3 \(144 \pi \mathrm{cm}^{2} / \mathrm{s}\)
4 none of these
Application of Derivatives

85130 The volume of a spherical ball is increasing at a rate of \(4 \pi \mathrm{cm}^{3} \mathrm{~s}^{-1}\). The rate at which its radius increases when its volume is \(288 \pi \mathrm{cm}^{3}\) is cm. \(\mathrm{s}^{-1}\)

1 \(1 / 6\)
2 \(1 / 36\)
3 \(1 / 9\)
4 \(1 / 24\)
[EAMCET 11.09.2020,Shift-II]
Application of Derivatives

85131 The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 \(\mathrm{cm}\) and \(20 \mathrm{~cm}\) respectively. If its diameter is increasing at a rate of \(2 \mathrm{~cm} / \mathrm{s}\), then at what rate must its altitude change in order to keep its volume constant?

1 \(4 \mathrm{~cm} / \mathrm{s}\)
2 \(6 \mathrm{~cm} / \mathrm{s}\)
3 \(-4 \mathrm{~cm} / \mathrm{s}\)
4 \(-8 \mathrm{~cm} / \mathrm{s}\)