Question

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Answer 1

Given :

• Diameter of cylinder A is 7 cm, and its height is 14 cm. Diameter of Cylinder B is 14 cm and its height is 7 cm.

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To Find :

• Without doing any calculation suggest that whose volume is greater. Verify it by finding the volume of cylinder .
• Check whether which cylinder has greater surface area and volume.

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Solution :

~ Grater Volume :

$\underline{\boxed{\pink{\textsf{ According to me Cylinder B has greater volume. }}}}$

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~ Formula Used :

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Volume{\tiny_{(Cylinder) }} = πr²h}}}}}$

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Surface \: Area{\tiny_{(Cylinder) }} = 2πr(r + h) }}}}}$

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~ Calculating the Volume :

Where :

• ➬ π = 22/7
• ➬ r = d/2 = 7/2 cm
• ➬ h = 14 cm

Calculation Starts :

${\longmapsto{\qquad{\sf{ Volume_A = πr²h }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_A = \dfrac{22}{7} \times \bigg\lgroup \dfrac{7}{2} \bigg\rgroup ^2 \times 14 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_A = \dfrac{22}{\cancel7} \times \bigg\lgroup \dfrac{7}{2} \bigg\rgroup ^2 \times \cancel{14} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_A = {\cancel{22} \times \dfrac{7}{\cancel2} \times \dfrac{7}{\cancel2} \times \cancel2 }}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_A = 11 \times 7 \times 7 \times 1 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_A = 77 \times 7 }}}} \\ \\ \ {\qquad{\sf{ Volume \: of \: Cylinder \: A \: = {\blue{\sf{ 539 \: cm² }}}}}}$

Here :

• ➬ π = 22/7
• ➬ r = 14/2 = 7 cm
• ➬ h = 7 cm

Calculation Starts :

${\longmapsto{\qquad{\sf{ Volume_B = πr²h }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_B = \dfrac{22}{7} \times 7^2 \times 7 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_B = \dfrac{22}{7} \times 7 \times 7 \times 7}}}} \\ \\ \ {\longmapsto{\qquad{\sf{Volume_B = \dfrac{22}{\cancel7} \times 49 \times \cancel7}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume_B = 22 \times 49 }}}} \\ \\ \ {\qquad{\sf{ Volume \: of \: Cylinder \: B \: = {\orange{\sf{ 1078 \: cm² }}}}}}$

Hence,

We verified that Volume of Cylinder B is Greater than A.

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~ Calculating Surface Area :

Cylinder A :

${\longmapsto{\qquad{\sf{ Surface \: Area_A = 2πr(r + h) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area_A = 2 \times \dfrac{22}{7} \times \dfrac{7}{2}(\dfrac{7}{2} + 14 ) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area_A = 2 \times \dfrac{22}{7} \times \dfrac{7}{2} \times \bigg\lgroup \dfrac{14 \times 2 + 7}{2} \bigg\rgroup }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area_A = \cancel{22} \times \dfrac{35}{\cancel2} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area_A = 11 \times 35 }}}} \\ \\ \ {\qquad{\sf{ Surface \: Area \: of \: A \: = {\pink{\sf{ 385 \: cm² }}}}}}$

Cylinder B :

${\longmapsto{\qquad{\sf{ Surface \: Area _B = 2πr(r + h) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area_B = 2 \times \dfrac{22}{7} \times 7 \bigg\lgroup 7 + 7 \bigg\rgroup }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area \: = 2 \times \dfrac{22}{7} \times 7 \times 14 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area \: = 2 \times \dfrac{22}{\cancel7} \times \cancel7 \times 14 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Surface \: Area \: = 2 \times 22 \times 14}}}} \\ \\ \ {\qquad{\sf{ Surface \: Area \: of \: B \: = {\red{\sf{ 616 \: cm² }}}}}}$

Hence,

Cylinder B has the grater surface Area.

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Therefore :

❝ Cylinder B is grater in both Volume and Surface Area as well. ❞

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Answer 2

Suggestion

I think that the volume of cylinder B will be greater.

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Verifying

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Volume for Cylinder A

Diameter = 7cm

Radius = $\sf\dfrac{diameter}{2} =\dfrac{7}{2}$

Height = 14cm

Volume = ?

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V = πr²h

V = $π\sf\Bigg(\dfrac{7}{2}²\Bigg) × 14$

V = $π\Bigg(\dfrac{49}{4}\Bigg) × 14$

V = $\sf\dfrac{22}{7} × \dfrac{49}{4}× 14$

V = 11 × 7 × 7

V = 539cm³.

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Volume for Cylinder B

Diameter = 14cm

Radius = $\sf\dfrac{diameter}{2}= \dfrac{14}{2}= 7$

Height = 7cm

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V = πr²h

V = π(7)²×7

V = π(49)×7

V = $\sf\dfrac{22}{7}× 49 × 7$

V = 22 × 7 × 7

V = 1078cm³.

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Hence, verified that the volume of Cylinder B is greater.

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Checking

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Surface Area for Cylinder A

Radius = $\sf\dfrac{7}{2}$

Height = 14cm

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SA = 2πrh+2πr²

$\sf{SA = \Bigg(2 \times \frac{22}{7}× \frac{7}{2}×14}\Bigg) + \Bigg(2 \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \Bigg)$

SA = (22×14) + (11×7)

SA = 308 + 77

SA = 385cm².

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Surface Area for Cylinder B

Radius = 7cm

Height = 7cm

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SA = 2πrh+2πr²

$\sf{SA =\Bigg(2 \times \frac{22}{7}} \times 7 \times 7\Bigg) + \Bigg(2 \times \frac{22}{7} \times 7 \times 7\Bigg)$

SA = (2×22×7) + (2×22×7)

SA = 308 + 308

SA = 616cm².

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Hence, checked that the cylinder with greater volume also has greater surface area.

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Thus, solved! ✓.

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