Question

A solid metal cuboid has length 44 cm, width 10 cm and height 5 cm.
The cuboid is melted down and all the metal is used to make a solid cylinder,of height 7 cm.
calculate the radius of the cylinder.
( use pi = 22/7)

1. minhkhue
Step-by-step explanation:
The volume of the cuboid is determined by multiplying the dimensions together:
V(cuboid) = l * w * h
44 * 10 * 5 = 2200
The value above is equivalent to the volume of the cylinder produced.
This formula determines the volume of the cylinder:  V = πr^2h
Substitute V for the volume given, which is 2200
2200 = πr^2h
Plug in 22/7 for pi and 7 for h
2200 = 22/7(r^2)7
2200 = (22/7 * 7)(r^2)
2200 = 22(r^2)
100 = r^2
Solve by taking the square root
√100 = 10
The radius should be equal to 10cm.
To double-check:
Use the same volume formula
V = (22/7)*(10^2)(7)
V = 22*100 = 2200

2. The radius of the cylinder is 10 cm.
Explanation:
Solid metal cuboid has length 44 cm, width 10 cm and height 5 cm.
That means, the volume of a metallic cuboid of sides = l × b × h
= 44 x 10 x 5
= 2200 cm³
The cuboid is melted down and all the metal is used to make a solid cylinder, Therefore the volume remains unchanged.
Given that, height of the cylinder = 7 cm.
Volume of cylinder = πr²h = 2200
πr²(7) = 2200
(22/7) r² (7) = 2200
r² = 100 cm²
r = 10 cm
Therefore, the radius of the cylinder is 10 cm.