Select all the common denominators for

1

4

and

7

10

.

a.

10

b.

20

c.

24

d.

32

e.

40

B, E

Step-by-step explanation:

There are a few ways to check for common denominator.

Here is one method

Take the 4 and 10 and see if both numbers will  go into the numbers evenly. If they do, it is a common denominator

Will 4 and 10 divide evenly into 10 ?

4 will not go into 10 evenly

10 is not a common denominator.

Will 4 and 10 divide evenly into 20?

4 will go into 20 evenly. 20 /4 = 5

10 will go into 20 evenly 20 / 10 =  2

So 20 is a common denominator

Will 4 and 10 divide evenly into 24?

4 will go into 24 evenly 24 / 4 = 6

10 will not go into 24 evenly

24 is not a common denominator

Will 4 and 10 divide evenly into 32?

4 will go into 32 evenly 32 / 4 = 8

10 will not go into 32 evenly

32 is not a common denominator

Will 4 and 10 divide evenly into 40?

4 will go into 40 evenly 40/4 = 10

10 will go into 40 evenly 40 / 10 = 4

40 is a common denominator

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.