Question

A toy is in the shape of a cylinder surmounted by a hemisphere. The height of the toy is 25cm. Find the total surface area of the toy if its common diameter is 12cm.

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Answer 1

Answer:

★Let r and h be the radius and height of the cylinder respectively.

★Given that, diameter d = 12cm, radius r = 6cm

★Total height of the toy is 25 cm

Therefore, the height of the cylindrical portion = 25 - 6 = 19cm

T.S.A of the toy = C.S.A of the cylinder + C.S.A of the hemisphere + Base Area of the cylinder

= 2πrh + 2πr² + πr²

= πr (2h + 3r) sq.units

= \frac{22}{7} \times 6 \times (38 + 18)=

7

22

×6×(38+18)

= \frac{22}{7} \times 6 \times 56=

7

22

×6×56

= 1056=1056

Therefore, T.S.A of the toy is 1056 cm².

Answer 2

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Question:

A toy is in the shape of a cylinder surmounted by a hemisphere. The height of the toy is 25cm. Find the total surface area of the toy if its common diameter is 12cm.

Solution:

T.S.A = C.S.A of hemisphere + C. S. A of cylinder + πr²

= 2πr² + 2πrh + πr²

= πr [2r + 2h + r ]

= 22/7 × 6 [2×6+2×19+6]

=22/7 × 6 [12+38+6]

=22/7 × 6 × 56

By canceling 7 and 56, we get:

1056cm³

Therefore, T.S.A of the toy is 1056 cm³.