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Solved Examples
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 c   A(x) = x2 + 8x represents the area of cross section perpendicular to x-axis of a solid when x represents the distance of cross section from the origin. What is the volume of the solid bounded by x = 5, x = 7?   c View Solution
 c   A square based pyramid of height 3 cm is resting on x-axis so that its square cross sections are perpendicular to x-axis. The vertex of the pyramid is on the plane x = 3 and the base of it is on the plane x = 5. If x is the distance from origin to the cross section, then the area of the cross section is 12x2. Find the volume of the pyramid.   c View Solution
 c   A solid is lying alongside the interval [0, π4] on the y-axis. 4sec y tan y is the area of the cross section of the solid perpendicular to the y-axis at the point y of [0, π4]. What is the volume of the solid?   c View Solution
 c   If x is the distance from the origin to the cross section perpendicular to x-axis of a solid, then 18 cos x represents the area of cross section. What is the volume of the solid between the planes x = π3 and x = π2 ?   c View Solution
 c   A(x) = 11tan x is the area of cross section perpendicular to the x-axis of a solid, where x is the distance of the cross section from the origin. What is the volume of the solid between the planes x = π6 to x = π3 ?   c View Solution
 c   What is the volume of a body bounded by the planes x = 3, x = 6 whose area of cross section perpendicular to x-axis is inversely proportional to the square of the distance of the section from the origin and the area of the cross section at x = 5 is 36 square units?   c View Solution
 c   If x is the distance from the origin to the cross section perpendicular to x-axis of a solid, then x2 represents the area of the cross section. Find the volume of the solid between the planes x = 2, x = 4 .   c View Solution
 c   What is the volume of a solid bounded by the planes x = 1, x = 7 whose area of cross section perpendicular to x-axis is proportional to lnx where x is the distance of the cross section from the origin, and whose area of cross section is ln 8 square units at x = 2 ?   c View Solution
 c   The volume of a solid bounded by the planes x = π4, and x = π2, whose area of cross section perpendicular to the x-axis at x is 17sin x. Find the volume of the solid.   c View Solution
 c   A(x) = (4x) is the area of cross section perpendicular to the x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = 1, x = 11 .   c View Solution
 c   A solid is resting on the x-axis whose cross section is perpendicular to x-axis. The area of a cross section of the solid is given by sec2 9x where x represents the distance of the cross section from the origin. Find the volume of the solid between the planes x = 0, x = π4 .   c View Solution
 c   A(x) = 5sin x + 5cos x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = π6, x = π4 .   c View Solution
 c   The cross section of a cake is perpendicular to x-axis. The area of cross section of the cake, x cm distant from the origin is 34 x sin x cm2.The cake is bounded between the planes x = 0, x = π2. If the cost of 1 cm3 cake is \$4, then find the cost of the cake.   c View Solution
 c   A solid is resting on the x-axis whose cross section is perpendicular to x - axis. The area of the cross section of the solid is given by 13 x cos x where x represents the distance of the cross section from the origin. What is the volume of the solid in cubic units if it is bounded between the planes x = 0, x = π4?   c View Solution
 c   A(x) = kx4 is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the volume of the solid bounded between the planes x = 0, x = 5 is 2500 cubic units, then k = ?   c View Solution
 c   A(x) = kxex is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the volume of the solid bounded between the planes x = 0, x = 5 is (20e5 + 5)cubic units, then find the value of k.   c View Solution
 c   A(x) = 12xsec2x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = 0, x = π4 .   c View Solution
 c   A(x) = 15x2 + 4x + 8 is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = 1, x = 2, then what is its volume ?   c View Solution
 c   A(x) = 20x cosec2x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = π4, x = π2, then what is its volume ?   c View Solution
 c   Find the volume of a cone of radius r and height h .   c View Solution
 c   The base of a solid is a circle of radius 4 units. If each cross section of the solid perpendicular to the diameter AB of it is a square, then what is the volume of the solid ?   c View Solution
 c   What is the volume of a body bounded by the planes x = 3, x = 7 whose area of cross section perpendicular to x-axis is inversely proportional to the square of the distance of the section from the origin and the area of the cross section at x = 5 is 20 square units?   c View Solution
 c   A square based pyramid of height 8 cm is resting on x-axis so that its square cross sections are perpendicular to x-axis. The vertex of the pyramid is on the plane x = 3 and the base of it is on the plane x = 6. If x is the distance from origin to the cross section, then the area of the cross section is 12x2. Find the volume of the pyramid.   c View Solution
 c   If x is the distance from the origin to the cross section perpendicular to x-axis of a solid, then x2 represents the area of the cross section. Find the volume of the solid between the planes x = 1, x = 5 .   c View Solution
 c   A(x) = x2 + 10x represents the area of cross section perpendicular to x-axis of a solid when x represents the distance of cross section from the origin. What is the volume of the solid bounded by x = 2, x = 5?   c View Solution
 c   The base of a solid is a circle of radius 3 units. If each cross section of the solid perpendicular to the diameter AB of it is a semicircle, then find the volume of the solid .   c View Solution
 c   The base of a solid is a circle of radius 2 units. If each cross section of the solid perpendicular to the diameter AB of it is an equilateral triangle, then find the volume of the solid .   c View Solution
 c   A solid is lying alongside the interval [0, π4] on the y-axis. 6sec y tan y is the area of the cross section of the solid perpendicular to the y-axis at the point y of [0, π4]. What is the volume of the solid?   c View Solution
 c   What is the volume of a solid bounded by the planes x = 1, x = 2 whose area of cross section perpendicular to x-axis is proportional to lnx where x is the distance of the cross section from the origin, and whose area of cross section is ln 625 square units at x = 5 ?   c View Solution
 c   The volume of a solid bounded by the planes x = π4, and x = π2, whose area of cross section perpendicular to the x-axis at x is 13sin x. Find the volume of the solid.   c View Solution
 c   If x is the distance from the origin to the cross section perpendicular to x-axis of a solid, then 12 cos x represents the area of cross section. What is the volume of the solid between the planes x = π3 and x = π2 ?   c View Solution
 c   A(x) = 17tan x is the area of cross section perpendicular to the x-axis of a solid, where x is the distance of the cross section from the origin. What is the volume of the solid between the planes x = π6 to x = π3 ?   c View Solution
 c   A(x) = (7x) is the area of cross section perpendicular to the x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = 1, x = 19 .   c View Solution
 c   A solid is resting on the x-axis whose cross section is perpendicular to x-axis. The area of a cross section of the solid is given by sec2 13x where x represents the distance of the cross section from the origin. Find the volume of the solid between the planes x = 0, x = π4 .   c View Solution
 c   A(x) = 7sin x + 7cos x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = π6, x = π4 .   c View Solution
 c   The cross section of a cake is perpendicular to x-axis. The area of cross section of the cake, x cm distant from the origin is 29 x sin x cm2.The cake is bounded between the planes x = 0, x = π2. If the cost of 1 cm3 cake is \$4, then find the cost of the cake.   c View Solution
 c   A solid is resting on the x-axis whose cross section is perpendicular to x - axis. The area of the cross section of the solid is given by 9 x cos x where x represents the distance of the cross section from the origin. What is the volume of the solid in cubic units if it is bounded between the planes x = 0, x = π4?   c View Solution
 c   A(x) = kx3 is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the volume of the solid bounded between the planes x = 0, x = 4 is 320 cubic units, then k = ?   c View Solution
 c   A(x) = kxex is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the volume of the solid bounded between the planes x = 0, x = 7 is (30e7 + 5)cubic units, then find the value of k.   c View Solution
 c   A(x) = 8xsec2x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. Find the volume of the solid between the planes x = 0, x = π4 .   c View Solution
 c   A(x) = 12x2 + 6x + 2 is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = 3, x = 4, then what is its volume ?   c View Solution
 c   A(x) = 16x cosec2x is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = π4, x = π2, then what is its volume ?   c View Solution
 c   A(x) = x sin(π4+x) is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = 0, x = π4, then find its volume .   c View Solution
 fff A(x) = x cos ((π4) + x) is the area of the cross section perpendicular to x-axis of a solid where x is the distance of the cross section from the origin. If the solid is bounded between the planes x = 0, x = π4, then find its volume . fff View Solution