2. Diameter of cylinder Ais 7 cm, and the height is 14 cm. Diameter of
cylinder B is 14 cm and height is 7 cm. Without doing any calculations
can you suggest whose volume is greater? Verify it by finding the
volume of both the cylinders. Check whether the cylinder with greater
volume also has greater surface area?
Answers
The heights and diameter of these cylinders A and B are interchanged.
We know that
Volume of cylinder =πr
2
h
If measures of r and h are same, then the cylinder with greater radius will have greater area.
Radius of cylinder A =
2
7
cm
Radius of cylinder B =
2
14
=7 cm
As the radius of cylinder B is greater,
therefore, the volume of cylinder B will be greater.
Let us verify it
Volume of cylinder A =πrh
=
7
22
×
2
7
×
2
7
×14
=539 cm
3
Volume of cylinder B =πr
2
h
=
7
22
×7×7×7
=1078 cm
3
Thus, volume of cylinder B is greater.
Surface area of cylinder A =2πr(r+h)
=2×
7
22
×
2
7
(
2
7
+14)
=22×(
2
7+28
)
=22×
2
35
=385 cm
2
Surface area of cylinder B =2πr(r+h)
=2×
7
22
×7×(7+7)
=44×14
=616 cm
Step-by-step explanation:
cylinder A
diameter of cylinder = 7 =r = 7/2cm
height = h = 14cm
cylinder B
diameter = 14cm = R = 7
height = H = 7cm
volume of cylinder = πr^2h
cylinder A and cylinder B
22/7 × 7/2 × 7/2 × 14
11 × 7 ×7
=539
22/7 × 7 × 7×7
22×7×7
=1078
volume of cylinder B is greater
T S A of cylinder A
surface area of cone = 2πr(r+h)
=2 × 22/7 × 7/2 ( 7/2 + 14 )
= 22 ( 35/2)
=11 × 35
=385
T S A of cylinder B
2 × 22/7 × 7 (7 + 7)
= 2× 22 × 14
=44 × 14
=616
cylinder B has greater T S A
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