Amonument in the form of a marble cylinder has a circular base with a radius of 1.5 meters. the altitude of the monument is 3.5 meters. how many cubic meters of marble does this monument contain? a. 7.07 m3 b. 24.74 m3 c. 21.21 m3 d. 6.19 m3

Option B. 24.74 m³

Step-by-step explanation:

A monument in the form of a marble cylinder has a circular base with radius = 1.5 meters

Altitude of the monument = 3.5 meters

Marble required to prepare the monument = Volume of the monument

                                                                       = π r² h

                                                                       = (3.14)(1.5)²(3.5)

                                                                       = 24.74 m³

Therefore, Option B. 24.74 m³ will be the answer.

10000

step-by-step explanation: divide by 2,

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.