Question

Diameter of cylinder A is 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?
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Answer 1

Answer:

The volume of cylinder A = 538.78 cm³

The volume of cylinder B = 1077.57 cm³

The surface area of cylinder A = 384.85 cm²

The surface area of cylinder B = 615.75 cm²

The cylinder with greater volume also has a greater surface area.

Step-by-step explanation:

It is given that the diameter of cylinder A is 7 cm, and the height is 14 cm.

And the diameter of cylinder B is 14 cm and the height is 7 cm.

Without doing any calculations I can suggest that among the volumes of the 2 cylinders, cylinder B has greater volume. Because the radius of cylinder B is greater than that of cylinder A and in the volume of the cylinder the radius is squared before multiplication.

⇒ The volume of a cylinder can be found by the following formula.

        V = πr²h

⇒ Therefore, the volume of cylinder A,

 $r =\dfrac{7}{2} = 3.5\ cm$

 h = 14 cm

 π = 3.14

         V = 3.14 × (3.5)² × 14

            = 538.78 cm³

⇒ The volume of cylinder B,

 $r =\dfrac{14}{2} = 7\ cm$

 h = 7 cm

 π = 3.14

         V = 3.14 × (7)² × 7

            = 1077.57 cm³

 Hence it is verified that cylinder B has greater volume.

⇒ The surface area of the cylinder (A) can be found by the following formula,

        A = 2πr(h + r)

⇒ The surface area of cylinder A

        A = (2 × 3.14 × 3.5) (14 + 3.5)

           = 384.85 cm²

⇒ The surface area of cylinder B

        A = (2 × 3.14 × 7) (7 + 7)

           = 615.75 cm²

Hence the cylinder with greater volume also has a greater surface area.