Question

Mayank made a bird bath for his garden in the shape of a cylinder with a hemispherical depression at one end as shown in the figure. The height of the hollow cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird bath. \[\left( {{\text{Take }}\pi = \dfrac{{22}}{7}} \right)\]

Answer 1

Hint: Cylinder is open from top and bottom. So, the area of top and bottom should not be included in the total surface area of the bird bath.

Complete step-by-step answer:
As we know that bird bath is open from the top.
And we can see from the above figure that the bird bath is also opened from the bottom.
And as we know that the total surface area of any figure is the sum of areas of all its surfaces.
So, now as we can see from the figure that bird bath consists of a hemispherical depression and a cylinder.
So, from the above figure we can clearly see that,
The total surface area of the bird bath = curved surface area of the hemispherical depression + curved surface area of the cylinder.
And as we know that the curved surface area of the cylinder having height h and radius r will be equal to 2[{\text{\pi }}\]rh.
As we know that here the radius of the cylinder and the hemisphere is 30 cm = 0.30 m.
And the height of the cylinder is 1.45 m.
So, curved surface area of the above cylinder will be $ 2 \pi * 0.3 *1.45 = 2.734 m^2 $.
As we know that the curved surface area of the hemisphere having radius r is given as $2\pi r^2 $
So, the curved surface area of the given hemispherical depression will be $ 2 \pi * (0.3)^2 = 0.566 m^2 $.
Hence, the curved surface area of the given bird bath will be $ (2.734 + 0.566) m^2 = 3.3 m^2 $.

Note: Whenever we come up with this type of the problem then first, we break the given figure into different known figures (like hemisphere and cylinder here) and after that we had to find the area of the that figure by using formulas like curved surface area of the cylinder is $ 2\pi rh $ and the curved surface area of hemisphere is $ 2\pi r^2$, where r is the radius and h is the height. This will be the efficient way to find the total surface area of the bird bath.