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Question : A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.​

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Answer 1

Answer:

Step-by-step explanation:

Given,

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder.

To Find,

Inner surface area.

Formula to be used,

CSA of cylinder = 2πrh

CSA of hemisphere = 2πr²

Solution,

Here,

We can clearly observe that radius of the cylindrical part and the hemispherical part are the same.

Height of hemispherical part = 7 cm

Height of cylindrical part = 13 - 7 = 6 cm

Inner surface area = CSA of cylinder + CSA of hemisphere

⇒ Inner surface area = 2πrh + 2πr²

⇒ Inner surface area = 2 × 22/7 × 7 × 6 + 2 × 22/7 × 7 × 7

⇒ Inner surface area = 44 × (6 + 7)

⇒ Inner surface area = 44 × 13

⇒ Inner surface area = 572 cm².

Hence, the Inner surface area of the vessel is 572 cm².

Answer 2

Answer:

Given :-

• A vessel is the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm.

To Find :-

• What is the inner surface area of the vessel.

Formula Used :-

✯ C.S.A of hemisphere = 2πr² ✯

★ C.S.A of cylinder = 2πrh ★

where,

• C.S.A = Curved Surface Area

Solution :-

First, we have to find the radius of the hemisphere,

As we know that,

✧ Radius = Diameter/2 ✧

Then,

⇒ Radius = 14/2

➠ Radius = 7 cm

Now, we have to find the curved surface area of hemisphere,

Given :

• Radius = 7 cm

According to the question by using the formula we get,

↦ C.S.A of hemisphere = 2 × 22/7 × (7)²

↦ C.S.A of hemisphere = 44/7 × 49

↦ C.S.A of hemisphere = 44 × 7

➦ C.S.A of hemisphere = 308 cm²

Hence, the curved surface area of hemisphere is 308 cm² .

Again, we have to find the curved surface area of cylinder,

As we know that,

✔ Radius of cylinder = Radius of hemisphere

where,

• r = 7

And,

✔ Height of cylinder = Total height - Radius of hemisphere

↪ 13 - 7

➤ 6 cm

Given :

• Radius = 7 cm
• Height = 6 cm

According to the question by using the formula we get,

↦ C.S.A of cylinder = 2 × 22/7 × 7 × 6

↦ C.S.A of cylinder = 44/7 × 42

↦ C.S.A of cylinder = 44 × 6

➦ C.S.A of cylinder = 264 cm²

Hence, the curved surface area of cylinder is 264 cm² .

Now, we have to find the inner surface area of vessel,

As we know that,

✪ Inner surface area = C.S.A of hemisphere + C.S.A of cylinder ✪

where,

• C.S.A = Curved Surface Area

According to the question by using the formula we get,

↪ 308 + 264

➦ 572 cm²

∴ The inner surface area of the vessel is 572 cm² .