Question

1. The volume of a right circular cylinder is 1100 cm³ and the radius of its base is 5 cm. Calculate its curved surface area.

2. What is the smallest number by which 256 may be divided so that the quotient is perfect cube?

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Answer 1

Answer :-

1. 440 cm2
2. 4

Solution :-

#1

• Volume of a right circular cylinder = 1100 cm³
• πr² h = 1100 cm³
• Here r = 5
• (22/7) ⋅ (5)² ⋅ h = 1100
• h = 2/7
• Curved surface area of cylinder = 2 πr h
• 2 ⋅ (22/7) ⋅ 5 ⋅ (2/7)
• 440 cm²

♧ So, the curved surface area of cylinder is 440²

#2

• To find the number required to divide 256 such that the quotient is a perfect cube, we have to decompose 256 into prime factors.

`\sf\longmapsto \sqrt[3]{256}`

• When we group the prime factors inside the cube root as triples, we left over with 2⋅ 2. That is 4.
• Hence 4 is the smallest number required to divide 256 so that the quotient is a perfect cube.

Hope it helps