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Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.

Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases. Correct Answer Only B and C

GIVEN:

Three statements.

CONCEPT:

Properties of cone and cylinder.

FORMULA USED:

Curved surface area of a cone = πrl

Total surface area of the cone = πr(l + r)

CALCULATION:

A:

Let the radius of circle be r cm

Original height be h

Volume = πr2h

When the radius is decreased by 50%

New radius = r – (50/100) × r = 0.5r

According to the question,

πr2h = π0.25r2h(new)

⇒ height is increased by 300%

∴ When radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 300%

B: The curved surface area of a cone is ‘πrl’ and the total surface area of the cone is ‘πr(l + r)’. The difference between both the areas will be (πrl + πr2 – πrl) = πr2.

C: In a cylinder, if height (h) is equal to its radius (r), then the curved surface area will be 2πrh = 2πr2 and its total area of both the circular bases will be πr2 + πr2 = 2πr2.

So, its curved surface area will be equal to the total area of its both the circular bases.

Hence, only B and C are TRUE.

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