व्हाट इज द क्वेश्चन वॉल्यूम क्वेश्चन एंड
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Answer:
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Hint: Let us assume the radius and height of the cylinder as ‘r’ and h respectively. We have given the volume and curved surface area of the cylinder. We know that the formula for the volume of the cylinder is πr2h and the formula for the curved surface area is 2πrh. Now, equating the volume and curved surface area that we have just mentioned to 1650 and 660. Now, we have two equations and two unknowns so we can find the value of r and h.
Complete step-by-step solution:
We have given the volume and curved surface area of the cylinder as 1650 cubic cm and 660 sq. cm respectively.
Let us assume that the radius and height of the cylinder are r and h respectively.
In the below diagram, we have shown a cylinder with radius (r) and height (h).
We know the formula for volume of the cylinder is equal to:
πr2h
Equating the above volume to 1650 we get,
πr2h=1650……… Eq. (1)
We know the formula for curved surface area of the cylinder is:
2πrh
Equating the above curved surface area to 660 we get,
2πrh=660…………. Eq. (2)
Now, we have two equations and two unknowns r and h which we are going to solve by dividing eq. (1) by eq. (2).
πr2h2πrh=1650660
In the above equation, π,r,h will be cancelled out from the numerator and the denominator we get,
r2=16566
Multiplying 2 on both the sides we get
r=165×266=33066⇒r=5cm
Substituting the above value of r in eq. (2) we get,
2π(5)h=660
Substituting the value of π as 227 in the above equation we get,
2(227)(5)h=660⇒2207h=660
Cross multiplying the above equation we get,
220h=660(7)⇒220h=4620⇒h=4620220⇒h=21cm
Hence, we have got the value of radius (r) as 5 cm and height (h) as 21 cm.
Note: You can verify that the value of the radius and height of the cylinder that you solved above is correct or not by substituting these values in the formula of the curved surface area of the cylinder.
The formula of curved surface area for cylinder is equal to:
2πrh
Substituting the value of r and h as 5 cm and 21 cm respectively in the above equation we get,
2(227)(5)(21)
21 will be cancelled out 3 times by 7 in the above expression and we get,
2(22)(5)(3)=660cm2
Now, as you can see in the question given above, the curved surface area of the cylinder is 660cm2 which is matching with the value of curved surface area that we have just calculated by putting r and h as 5cm and 21 cm respectively.
Hence, the value of the radius and height of the cylinder that we are getting is correct.
Explanation:
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