Answer to Question #147881 in Trigonometry for yui

Question

 

(NOS. 2-5) PROBLEM 1. A cylindrical container of height equal to twice the diameter of its base can hold            12 liters (1L= 1,000 cm³) of water. Another cylindrical container with the same capacity has its            height equal to three times the diameter of its base.

 

______________________   2) What is the diameter of the first container in cm?

 

_______________________ 3) What is the diameter of the second container in cm?

 

Answer 1

Trigonometry

Solution

Diameter = d

Height = h

Radius = r

Volume = V = 12L = 12000cm³

2. h = 2d and d= 2r

Therefore, h = 2 x 2r = 4r

V = πr²h = πr² x 4r

V = 4πr³ = 12000cm³

r³ = 12000cm³ /4π

r³ = 954.93cm³

r = 9.85cm

d = 2r = 2 x 9.85 = 19.7cm

3. h = 3d and d= 2r

Therefore, h = 3 x 2r = 6r

V = πr²h = πr² x 6r

V = 6πr³ = 12000cm³

r³ = 12000cm³ /6π

r³ = 636.62cm³

r = 8.6cm

d = 2r = 2 x 8.6 = 17.2cm