Q. 194.5( 6 Votes )

Answer :

**Given:** The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m^{2 }and the pipe is made of 99 cm^{3} of metal.**To find: **the outer and inner radii of the pipe.**Solution:**

Let the inner radius of pipe = r1

And the radius of outer cylinder = r2

Length of cylinder (h) = 14 cm

Surface area of hollow cylinder =2πh (r2 –r1)

Given surface area of cylinder = 44 m^{2}.

⇒ 2π h(r2 –r1) = 44

⇒ 2π (14) (r2 –r1) = 44

⇒ (r2 –r1) =

⇒ (r2 –r1) =

⇒ (r2 –r1) =

⇒ (r2 –r1) = 1/2 ……. (1)

Given volume of a hollow cylinder = 99 cm^{3}

Volume of a hollow cylinder = π h()

⇒ π h (r2^{2} - r1^{2}) = 99

⇒ 14π (r2^{2} - r1^{2}) = 99

Apply the formula a^{2} - b^{2} = ( a - b ) ( a + b ) in (r2^{2} - r1^{2}).

⇒ 14π (r2 + r1) (r2 – r1) = 99

Put the value of r2 - r1 from (1).

⇒ 14π (r2 + r1) = 99

⇒ 22 (r2+r1) = 99

⇒ (r2+r1) = ……………… (2)

Equating (1) & (2) equations we get

r2 = 5/2 cm

Substituting r2 value in (1)

⇒ r1 = 2 cm

∴Inner radius of pipe (r1) = 2 cm

Radius of outer cylinder (r2) = 5/2 cm

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSA toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.NEXTA right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

RELATED QUESTIONS :

The length of the diagonal of a cube is 6 √ 3 cm. Its total surface area is

RS Aggarwal - MathematicsThe diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is

RS Aggarwal - MathematicsThe curved surface area of a cylinder is 1760 cm^{2} and its base radius is 14 cm. The height of the cylinder is

The area of the base of a right circular cone is 154 cm^{2} and its height is 14cm. Its curved surface area is

The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is

RS Aggarwal - MathematicsA circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required is

RS Aggarwal - MathematicsThe volume of a hemisphere is 19404 cm^{3}. The total surface area of the hemisphere is