the difference between the outer and inner csa of a hollow right cylinder 14 cm long is 88cm square if volume of metal used in making the cylinder is 176cm square find the outer and inner diameter of the cylinder
Answers
Answer:
Height of a hollow right circular cylinder (h)= 14 cm
Difference between outer and inner closed surface area of a hollow right circular cylinder = 88 cm²
Volume of metal used in making cylinder= 176 cm³
Let external radius and inner radius be R and r.
Outer surface area of Hollow Cylinder - inner surface Area of Hollow Cylinder = 88 cm²
2π R h - 2π r h = 88
2πh (R - r) = 88
2× (22/7) × 14 (R - r) = 88
2 × 22 × 2 (R - r)
88 (R - r) = 88
R - r = 88/88 =
R - r = 1.........................(1)
Volume of Hollow Cylinder = π(R² - r² )h
176 = 22/7(R² - r² ) ×14
14× 22/ 7 {R² - r² } = 176
44 {R² - r² } = 176
{R² - r² } = 176/44
{R² - r²} = 4
{R - r} {R + r} = 4
[a² - b² = (a+b)(a -b)]
(1){R + r} = 4 [ from eq 1]
{R + r} = 4 …... ....................(2)
R - r = 1
R + r = 4 [ On Adding eq 1 & 2]
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2R = 5
R= 5/2
External Radius of hollow cylinder(R) = 5/2
On Putting the value of R in eq 1.
R - r = 1
5/2 - r = 1
5/2 -1 = r
(5 -2)/2 = r
r = 3/2
Internal Radius of hollow cylinder(R) = 3/2
EXTERNAL DIAMETER of hollow cylinder = radius /2 = (5/2) /2 = 5 cm
INNER DIAMETER of hollow cylinder = radius /2 = (3/2)/2 = 3 cm
Hence , the External & internal diameter of hollow cylinder = 5 cm & 3 cm.
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