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A solid cylinder has a total surface area of 462 m2. Its curved surface area is one-third of the total surface area. What is the volume of the cylinder?
- a)569 cm3
- b)539 cm3
- c)529 cm3
- d)549 cm3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A solid cylinder has a total surface area of 462 m2. Its curved surfac...
Given:
Total surface area of the cylinder = 462 m2
Curved surface area = 1/3 of the total surface area
To Find:
Volume of the cylinder
Solution:
Step 1: Find the Curved Surface Area
Curved surface area = 1/3 * Total surface area
Curved surface area = 1/3 * 462
Curved surface area = 154 m2
Step 2: Find the Curved Surface Area of the Cylinder
Curved surface area of a cylinder = 2πrh
Where r is the radius and h is the height of the cylinder
Step 3: Find the Height of the Cylinder
Let the radius be r and height be h
2πrh = 154
r = 7
h = 11
Step 4: Find the Volume of the Cylinder
Volume of a cylinder = πr2h
Volume = π * 7^2 * 11
Volume ≈ 539 cm3
Therefore, the volume of the cylinder is approximately 539 cm3.
Total surface area of the cylinder = 462 m2
Curved surface area = 1/3 of the total surface area
To Find:
Volume of the cylinder
Solution:
Step 1: Find the Curved Surface Area
Curved surface area = 1/3 * Total surface area
Curved surface area = 1/3 * 462
Curved surface area = 154 m2
Step 2: Find the Curved Surface Area of the Cylinder
Curved surface area of a cylinder = 2πrh
Where r is the radius and h is the height of the cylinder
Step 3: Find the Height of the Cylinder
Let the radius be r and height be h
2πrh = 154
r = 7
h = 11
Step 4: Find the Volume of the Cylinder
Volume of a cylinder = πr2h
Volume = π * 7^2 * 11
Volume ≈ 539 cm3
Therefore, the volume of the cylinder is approximately 539 cm3.
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Community Answer
A solid cylinder has a total surface area of 462 m2. Its curved surfac...
Curved surface area
= 1/3 × total surface area
= 1/3 × 462 = 154
⇒ 2πrh = 154 …(1)
Total surface area = 462
⇒ 2πrh + 2πr2 = 462
⇒ 154 + 2πr2 = 462
⇒ 2πr2 = 308
Putting this value in (i), we get
2πrh = 154
∴ Volume of cylinder
= 1/3 × total surface area
= 1/3 × 462 = 154
⇒ 2πrh = 154 …(1)
Total surface area = 462
⇒ 2πrh + 2πr2 = 462
⇒ 154 + 2πr2 = 462
⇒ 2πr2 = 308
Putting this value in (i), we get
2πrh = 154
∴ Volume of cylinder
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A solid cylinder has a total surface area of 462 m2. Its curved surface area is one-third of the total surface area. What is the volume of the cylinder?a)569 cm3b)539 cm3c)529 cm3d)549 cm3Correct answer is option 'B'. Can you explain this answer?
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