Question

The curved surface area of a right circular cylinder of height 21 cm is 528 sq. cm. Find the radius of the base of the cylinder. *​

Answer 1

Answer:

Radius of the base is 4 cm.

Step-by-step explanation:

Given :-

• The curved surface area of a right circular cylinder of height 21 cm is 528 cm².

To find :-

• The radius of the base of the cylinder.

Solution :-

Let the radius of the cylinder be r cm.

Formula used :

${\boxed{\sf{CSA\:of\:cylinder=2\pi rh}}}$

• Height = 21 cm
• CSA of the cylinder = 528 cm²

According to the question :-

$\to\sf\:2\pi rh = 528\\ \\ \to\sf\: 2\times\dfrac{22}{7} \times\:r\times 21=528\\ \\ \to\sf 2\times22\times r\times 3=528\\ \\ \to\sf 132r=528\\ \\ \to\sf r=4$

Therefore the radius of the cylinder is 4 cm.

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Additional Info :-

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²

Answer 2

✦ GIVEN :

curved surface area of a right circular cylinder= 528 cm²

height of circular cylinder = 21 cm

✦ TO FIND :

radius of the base of the cylinder

✦ FORMULA USED :

C.S.A of cylinder = 2πrh

where :-

• C.S.A = curved surface area
• r = radius of the base of cylinder
• h = height of cylinder

✦ SOLUTION :

☆ It is given that C.S.A and height of the cylinder are 528 cm² and 21cm respectively.

☆ Therefore put the given values in the FORMULA :-

$⟹C.S.A = 2πrh$

$⟹528 = 2πr \times 21$

$⟹528 = πr \times 42$

we know , π = 22/7

$⟹528 = \frac{22}{7} \times r \times 42$

$⟹ \frac{528 \times 7}{42 \times 22} = r$

$⟹ 4= r$

Therefore radius of base of cylinder = 4 cm

✦ ANSWER :

☆radius of base of cylinder = 4 cm

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✦ LEARN MORE :-

1. Volume of cylinder = πr²h

2. CSA = 2πrh

3. T.S.A of cylinder :-

= Curved surface area + area of base circles of both end

=> 2πrh + πr² + πr²

=> 2πrh + 2πr²

☆Therefore TSA of cylinder = 2πrh + 2πr²

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