The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm ² . If the volume of metal used in making the cylinder is 176 cm³, find the outer and inner diameters of the cylinder. (Use 
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Answers
Answer:
The outer and inner diameters of hollow cylinder = 5 cm & 3 cm.
Step-by-step explanation:
Given:
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)
On Adding eq 1 & 2,
R - r = 1
R + r = 4
-----------------
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 = 2 × radius = (5/2) × 2 = 5 cm
INNER DIAMETER of hollow cylinder =2 × radius = (3/2) × 2 = 3 cm
Hence , the outer and inner diameters of hollow cylinder = 5 cm & 3 cm.
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Answer:
Step-by-step explanation:
