Question

If the length of cylindrical part is 3 times the radius r of the
hemispherical part, then the curved surface area of the cylindrical
part of the boiler is:​

Answer 1

Answer:

c h tu

Step-by-step explanation:

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Answer 2

Answer:

Q.1. Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Sol. Volume of each cube = 64 cm3

∴ Total volume of the two cubes = 2 × 64 cm3

= 128 cm3

Let the edge of each cube = x

∴ x3 = 64 = 43

∴ x = 4 cm

Now, Length of the resulting cuboid l = 2x cm

Breadth of the resulting cuboid b = x cm

Height of the resulting cuboid h = x cm

∴ Surface area of the cuboid = 2 (lb + bh + hl) = 2[(2x . x) + (x . x) + (x . 2x)]

= 2[(2 × 4 × 4) + (4 × 4) + (4 × 2 × 4)] cm2

= 2 [32 + 16 + 32] cm2 = 2[80] cm2 = 160 cm2.

Q.2. 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.

Sol. For cylindrical part:

Radius (r) = 7 cm

Height (h) = 6 cm

∴ Curved surface area

= 2πrh

For hemispherical part:

Radius (r) = 7 cm

∴ Surface area = 2πr2

∴ Total surface area

= (264 + 308) cm2 = 572 cm2.

Q.3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Sol. Here, r = 3.5 cm

∴ h = (15.5 – 3.5) cm = 12.0 cm

Surface area of the conical part

= πrl

Surface area of the hemispherical part

= 2πr2

∴ Total surface area of the toy

= πrl + 2πr2 = πr (l + 2r) cm2

∵ l2 = (12)2 + (3.5)2

Q.4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Sol. Side of the block = 7 cm

⇒ The greatest diameter of the hemisphere = 7 cm

Surface area of the solid

= [Total S.A. of the cubical block] + [S.A. of the hemisphere] – [Base area of the hemisphere]

= (6 × l2) + 2πr2 – πr2

Q.5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Sol. Let ‘l’ be the side of the cube.

∴ The greatest diameter of the curved hemisphere = l