Click on a 'View Solution' below for other questions:

e A(x) = x^{2} + 8x represents the area of cross section perpendicular to xaxis 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? e

View Solution 

e A square based pyramid of height 3 cm is resting on xaxis so that its square cross sections are perpendicular to xaxis. 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 12x^{2}. Find the volume of the pyramid. e

View Solution 

e A solid is lying alongside the interval [0, π4] on the yaxis. 4sec y tan y is the area of the cross section of the solid perpendicular to the yaxis at the point y of [0, π4]. What is the volume of the solid? e

View Solution 

e If x is the distance from the origin to the cross section perpendicular to xaxis 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 ? e

View Solution 

e A(x) = 11tan x is the area of cross section perpendicular to the xaxis 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 ? e

View Solution 

e What is the volume of a body bounded by the planes x = 3, x = 6 whose area of cross section perpendicular to xaxis 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? e

View Solution 

e If x is the distance from the origin to the cross section perpendicular to xaxis of a solid, then x^{2} represents the area of the cross section. Find the volume of the solid between the planes x = 2, x = 4 . e

View Solution 

e What is the volume of a solid bounded by the planes x = 1, x = 7 whose area of cross section perpendicular to xaxis 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 ? e

View Solution 

e The volume of a solid bounded by the planes x = π4, and x = π2, whose area of cross section perpendicular to the xaxis at x is 17sin x. Find the volume of the solid. e

View Solution 

e A(x) = (4x) is the area of cross section perpendicular to the xaxis 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 . e

View Solution 

e A solid is resting on the xaxis whose cross section is perpendicular to xaxis. The area of a cross section of the solid is given by sec^{2} 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 . e

View Solution 

e A(x) = 5sin x + 5cos x is the area of the cross section perpendicular to xaxis 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 . e

View Solution 

e The cross section of a cake is perpendicular to xaxis. The area of cross section of the cake, x cm distant from the origin is 34 x sin x cm^{2}.The cake is bounded between the planes x = 0, x = π2. If the cost of 1 cm^{3} cake is $4, then find the cost of the cake. e

View Solution 

e A solid is resting on the xaxis 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? e

View Solution 

e A(x) = kx^{4} is the area of the cross section perpendicular to xaxis 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 = ? e

View Solution 

e A(x) = kxe^{x} is the area of the cross section perpendicular to xaxis 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 (20e^{5} + 5)cubic units, then find the value of k. e

View Solution 

e A(x) = 12xsec^{2}x is the area of the cross section perpendicular to xaxis 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 . e

View Solution 

e A(x) = 15x^{2} + 4x + 8 is the area of the cross section perpendicular to xaxis 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 ? e

View Solution 

e A(x) = 20x cosec^{2}x is the area of the cross section perpendicular to xaxis 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 ? e

View Solution 

e Find the volume of a cone of radius r and height h . e

View Solution 

e 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 ? e

View Solution 

e What is the volume of a body bounded by the planes x = 3, x = 7 whose area of cross section perpendicular to xaxis 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? e

View Solution 

e A square based pyramid of height 8 cm is resting on xaxis so that its square cross sections are perpendicular to xaxis. 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 12x^{2}. Find the volume of the pyramid. e

View Solution 

e If x is the distance from the origin to the cross section perpendicular to xaxis of a solid, then x^{2} represents the area of the cross section. Find the volume of the solid between the planes x = 1, x = 5 . e

View Solution 

e A(x) = x^{2} + 10x represents the area of cross section perpendicular to xaxis 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? e

View Solution 

e 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 . e

View Solution 

e 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 . e

View Solution 

e A solid is lying alongside the interval [0, π4] on the yaxis. 6sec y tan y is the area of the cross section of the solid perpendicular to the yaxis at the point y of [0, π4]. What is the volume of the solid? e

View Solution 

e What is the volume of a solid bounded by the planes x = 1, x = 2 whose area of cross section perpendicular to xaxis 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 ? e

View Solution 

e The volume of a solid bounded by the planes x = π4, and x = π2, whose area of cross section perpendicular to the xaxis at x is 13sin x. Find the volume of the solid. e

View Solution 

e If x is the distance from the origin to the cross section perpendicular to xaxis 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 ? e

View Solution 

e A(x) = 17tan x is the area of cross section perpendicular to the xaxis 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 ? e

View Solution 

e A(x) = (7x) is the area of cross section perpendicular to the xaxis 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 . e

View Solution 

e A solid is resting on the xaxis whose cross section is perpendicular to xaxis. The area of a cross section of the solid is given by sec^{2} 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 . e

View Solution 

e A(x) = 7sin x + 7cos x is the area of the cross section perpendicular to xaxis 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 . e

View Solution 

e The cross section of a cake is perpendicular to xaxis. The area of cross section of the cake, x cm distant from the origin is 29 x sin x cm^{2}.The cake is bounded between the planes x = 0, x = π2. If the cost of 1 cm^{3} cake is $4, then find the cost of the cake. e

View Solution 

e A solid is resting on the xaxis 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? e

View Solution 

e A(x) = kx^{3} is the area of the cross section perpendicular to xaxis 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 = ? e

View Solution 

e A(x) = kxe^{x} is the area of the cross section perpendicular to xaxis 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 (30e^{7} + 5)cubic units, then find the value of k. e

View Solution 

e A(x) = 8xsec^{2}x is the area of the cross section perpendicular to xaxis 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 . e

View Solution 

e A(x) = 12x^{2} + 6x + 2 is the area of the cross section perpendicular to xaxis 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 ? e

View Solution 

e A(x) = 16x cosec^{2}x is the area of the cross section perpendicular to xaxis 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 ? e

View Solution 

e A(x) = x sin(π4+x) is the area of the cross section perpendicular to xaxis 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 . e

View Solution 

e A(x) = x cos ((π4) + x) is the area of the cross section perpendicular to xaxis 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 . e

View Solution 
