1. Height of a cylinder is double the radius and its volume is 2156 m3. Find the dimensions of the cylinder.
2. If the radius of a cylinder is doubled, what will be the ratio between the volume of the new cylinder to the volume of the original one?
3. If radius and height both are doubled, find the ratio between the volumes of the new with the original cylinder.
4. The capacity of a cylindrical tank is 924 m3 and radius of the base is 7 m. Find its height.
5. To make a cylinder of height 10 cm and radius 3 cm, how many coins of radius 1 cm and thickness 2 mm will have to be melted?
Answers
Answer:
Step-by-step explanation:
1) cylinder
r = x then h = 2x , given V = 2156
volume = 2156
π r² h = 2156
π x X² x 2X = 2156
X³ = 343
X = 7
dimensions of cylinder
r = 7m , h = 14m
2) r = 14m h =14m
volume of new = 22/7 x 14 x14 x14
= 8624
volume of new : volume of original
8624 : 2156
4 : 1
3) r=14 m h= 28m
volume of new = 22/7 x14 x14 x28
= 17248 m³
volume of new : volume of original
17248 : 2156
8 : 1
4) r = 7m volume = 924m³ h=?
volume = 924
π r² h = 924
22/7 x 7x 7 xh =924
h = 6m
5) r = 3cm , h = 10cm coins ⇒ r = 1cm , h = 0,2 cm
number of coins = volume of cylinder / volume of coins
= ( π x3 x3 x10) / (π x 1 x1x 0.2)
= 450 coins