Question

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.

Answer 1

Given that a wooden article is made by scooping out a hemisphere each from the top and bottom of a solid cylinder with $h=10cmandr=3.5cm$

To find out: The total surface area of the article.

Total surface area of the article $=$ Lateral surface area of cylinder $+2\times$ Curved surface area of hemisphere

We know that the lateral surface are of a cylinder $=2\pi rh$.

And the curved surface area of a hemisphere $=2\pi r^2$.

$\therefore$ TSA of article $=2\pi rh+2\times 2\pi r^2$

$\Rightarrow 2\times \frac{22}{7}\times \frac{7}{2}\times 10+2\times 2\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2$

$\Rightarrow 22\times 10+22\times 7$

$\Rightarrow 22(10+7)$

$\Rightarrow 22\times 17$

$\therefore TSA=374c{m}^2$

Hence, the total surface area of the article is $374c{m}^2$.