The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
A. 24/√π
B. 48/√π
C. 32/√π
D.48/π
Answers
Given : The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out.
We know that ,there are 1728 cubic inches in a cubic foot.
1 cubic feet = 12 × 12 × 12 = 1728 inch³
Volume of sand = 1728 inch³
Volume of Cylinder = πr² ×3 inch ³
πr² × 3 = 1728
πr² = 1728/3
πr² = 576
r² = 576/π
r = √576/π
r = 24/√π
Radius = 24/√π
Diameter of cylinder ,d = 2r = 2 × 24/√π
d = 48/√π
Hence, the diameter, in inches, of the cylinder is 48/√π.
Option (B) 48/√π is correct ,
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Answer:
Given:
The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out.
To Find:
The diameter, in inches, of the cylinder
Solution:
We know that 1 cubic feet = 12 × 12 × 12 = 1728 inch³
Volume of sand = 1728 inch³
Volume of Cylinder = πr² ×3 inch ³
πr² × 3 = 1728
πr² = 1728/3
πr² = 576
r² = 576/π
r = √576/π
r = 24/√π
Radius = 24/√π
Diameter of cylinder ,d = 2r
= 2 × 24/√π
d = 48/√π