Application of Integration

Application of Integration - Set 1

Report 1 / 5

Calculate the volume generated when the shaded region in the diagram is rotated \(360\degree\) through \(y-\)axis.

(A)		\(\dfrac{65}{3} \pi \text{ unit}^3\)

(B)		\(\dfrac{55}{3} \pi \text{ unit}^3\)

(C)		\(\dfrac{25}{3} \pi \text{ unit}^3\)

(D)		\(\dfrac{85}{3} \pi \text{ unit}^3\)

Difficulty Level: Hard

Application of Integration - Set 1

Report 2 / 5

Find the volume generated when the shaded region in the diagram is rotated \(360\degree\) through \(y-\)axis.

(A)		\(50 \pi \text{ unit}^3\)

(B)		\(20 \pi \text{ unit}^3\)

(C)		\(40 \pi \text{ unit}^3\)

(D)		\(30 \pi \text{ unit}^3\)

Difficulty Level: Hard

Application of Integration - Set 1

Report 3 / 5

Calculate the volume of solid generated when the shaded region in the diagram is rotated \(360\degree\) through the \(x-\)axis.

(A)		\(127 \pi \text{ unit}^3\)

(B)		\(128 \pi \text{ unit}^3\)

(C)		\(129 \pi \text{ unit}^3\)

(D)		\(130 \pi \text{ unit}^3\)

Difficulty Level: Hard

Application of Integration - Set 1

Report 4 / 5

Given that the volume of solid generated when the shaded region in the diagram is rotated \(360\degree\) through the \(-y\) axis is \(\dfrac{9}{2} \pi \text{ unit}^3\).

Find the value of \(k\).

(A)		\(7\)

(B)		\(8\)

(C)		\(9\)

(D)		\(10\)

Difficulty Level: Hard

Application of Integration - Set 1

Report 5 / 5

Calculate the volume of solid generated when the shaded region in the diagram is rotated \(360\degree\) through the \(x-\)axis.

(A)		\(\dfrac{868}{5}\pi \text{ unit}^3\)

(B)		\(\dfrac{2\,068}{5}\pi \text{ unit}^3\)

(C)		\(\dfrac{968}{5}\pi \text{ unit}^3\)

(D)		\(\dfrac{1\,068}{5}\pi \text{ unit}^3\)

Difficulty Level: Hard