Simon calculated the volume of the prism. His work is shown here. area of base = B = 1 2 bh = 1 2 (5)(13) = 32.5 m2 volume = Bh = 32.5(12) = 390 m3 A triangular prism. The triangular base has a base of 5 meters and height of 12 meters. The height is 4 meters. What errors did he make? Check all that apply. The area of the base is 30 m2, not 32.5 m2. The area of the base is 60 m2, not 32.5 m2. The area of the base is 78 m2, not 32.5 m2. The volume of the prism is 108 m3, not 390 m3. The volume of the prism is 120 m3, not 390 m3.

a and e

Step-by-step explanation:

i got it right :)

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.