The base of a solid is a circular disk with radius 4. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.

the volume of the solid is 1024/3 cubic unit

Step-by-step explanation:

Given the data in the question,

radius of the circular disk = 4

Now if the center is at ( 0,0 ), the equation of the circle will be;

x² + y² = 4²

x² + y² = 16

we solve for y

y² = 16 - x²

y = ±√( 16 - x² )

{ positive is for the top while the negative is for the bottom position }

A = b²

b = 2√( 16 - x² )           { parallel cross section }

A = [2√( 16 - x² )]²

A = 4( 16 - x² )

Now,

VOLUME =

=

= 4[ 16x - (x³)/3 ]           { from -4 to 4 }

= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]

= 4[ 64 - 64/3 + 64 - 64/3 ]

= 4[ (192 - 64 + 192 - 64 ) / 3 ]

= 4[ 256 / 3 ]

= 1024/3 cubic unit

Therefore,  the volume of the solid is 1024/3 cubic unit

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.