a cylindrical tank of height equal to twice the diameter of its base can hold 10,000 cm^3 of water. another cylindrical container with the same capacity has its height equal to 3 times the diameter of its base. find the ratio of the amount of aluminum required for making the two containers including covers

Question

campbell_st · Answer

well look at the volume 1st and use the information to find the diameter

tank 1

d = diameter    r = d/2   then height = 2d or 4r

so the volume is 

$$v = \pi \times r^2 \times 4r$$

or 

$$10000 = 4\pi r^3$$

solve for r

tank 2 

d = diameter then r = d/2      height = 3d or 6r

use the volume information to find d

$$10000 = \pi \times r^2 \times 6r$$

or

$$10000 = 6\pi r^3$$

again solve for r. 

so now you have the diameter of each tank

now the surface area 

tank 1

$$SA = 2\pi r^2 + 2\pi r \times 4r$$

substitute the value of r you found from the volume of tank 1. 

tank 2

$$SA = 2\pi r^2 + 2\pi r \times  3r$$

substitute the value of r you found from take 2. 

then make the ratio of surface areas   tank 1 :tank 2

hope it helps