Question

a model shaped like a cylinder with 2 cones attached to its ends the diameter of. model is 3 cm and total height is 12cm if each cone has a height of 2 cm find surface area of model​

Answer 1

Answer:

For the given statement first draw a diagram,

In this diagram, we can observe that

Height (h1) of each conical part =2 cm

Height (h2) of cylindrical part 12−2−2=8 cm

Radius (r) of cylindrical part = Radius of conical part = 23 cm

Volume of air present in the model = Volume of cylinder + 2× Volume of a cone 

=πr2h2+2×πr2h1

=π(23)2×8+2×31π(23)2(2)

=π×49×8+32π×49×2

=18π+3π=21π

=21×722=66 cm2

Answer 2

Given :-

◉ A model shaped like a cylinder of height, h = 12 cm, its two ends are in the shape of a cone, of height, h₂ = 2 cm , and radius , r = 3/2 cm

To Find :-

◉ Surface area of model

Solution :-

According to the question,

Surface area of the model would be the sum of the curved surface area of the cylinder and the two cones.

⇒ Surface Area = 2πrh + πrl + πrl

⇒ Surface Area = 2πrh + 2πrl

⇒ Surface Area = 2πr ( h + l )

⇒ Surface Area = 2×π×3/2 ( 8 + √{2² + (3/2)²} )

⇒ Surface Area = 3π ( 8 + 5/2 )

⇒ Surface Area = 3 × 22/7 × 21/2

⇒ Surface Area = 3 × 11 × 3

⇒ Surface Area = 99 cm²

Hence, Surface area of the model is 99 cm².

Some Formulae :-

◉ Volume of Cube = ( Side )³

◉ Volume of Cuboid = L × B × H

Where, L = length, B = breadth, H = height

◉ Slant height l of a cone is √(h² + r²)

Where, h & r are height and radius of the cone respectively.

◉ Volume of Cone = 1/3 πr²h

◉ Volume of Cylinder = πr²h