# Question: 1a find the volume of the solid whose base is...

###### Question details

1a. Find the volume of the solid whose base is bounded by the functions f (x) =− x + 4 and g (x) = 2x^2+3 using cross sections perpendicular to the x axis that are rectangles with the base in the x-y plane and height equal to 4 times the base.

1b. Find the volume of the solid whose base is one side of an equilateral triangle that is perpendicular to the x-axis where the length is represented by the curve f (x) = cubed root√ (x+2) over the interval [-2, 4].

1c. Find the volume of the solid that has semi-circular cross sections perpendicular to the x-axis bounded by the curve f (x) =1/x over the interval [1, 8].

1d. Find the value of the solid whose base is a circle centered at the origin with radius of 4 using cross sections perpendicular to the y-axis that are isosceles right triangles with one leg in the coordinate plane.

1e. The base of a solid is the region in the first quadrant that is bound by the graph of y = 3 + cos(x) over the interval [0, π] . Find the volume using cross sections that are perpendicular to the x-axis, where the cross sections are isosceles right triangles with the hypotenuse in the coordinate plane.

Please explain how you found your answer. Thanks