Identify the number property. 1. 3x + 5 = 5 + 3x 2. 6 * (7 * 8) = (6 * 7) * 8 3. 9 + (6x + 11) = (6x + 11) + 9 4. if 7 = x, then x = 7 5. if x = 4 and 4 = y, then x = y 6. every real number is equal to itself name the property that justifies each step 1. (2* 93) * 5 = (93 * 2) * 5 = 93* (2 5) = 93 * 10 = 930 2. (26 + 71) + 14 = 26 + (71 + 14) = 26 + (14 + 71) = (26 + 14) + 71 = 40 + 71 = 111 3. 50 * (47 * 8) = 50 * (8 * 47) = (50 * 8)* 47 = 400 * 47 = (100 *4) * 47 = 100 * (4 * 47) = 100 * 188 = 18,800 4. [13 + 3] + (-3) = 13 + [3 + (-3)] = 13 + 0 =13 5. (17 * 5) * 1/5 = 17 * (5 * 1/5) = 17 * 1 = 17

step-by-step :

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.