B. 8/27 d. 1/3 10. three spheres of radii , 2r, and 3r, respectively, are melted and formed into a new sphere. find the surface area of this new sphere. a. 136.8 r(squared) c. 124.5 r(squared) b. 143.7 r(squared) d. 113.4 r(squared) 11. three spheres of radii r, 2r, and 3r, respectively, are melted and formed into a new sphere. find the volume of this new sphere. a. 54 pi r(cubed) c. 48 pi r(cubed) b. 43 pi r (cubed) d. 32 pi r(cubed)

Step-by-step explanation:

In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:

Now that we know the radii of the new sphere, we can calculate the surface area:

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.

you are uyytr tyy

step-by-step explanation: