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A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown below. 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
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## QuestionMathsClass 10

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown below. 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

$$374\ m^2$$
4.6
4.6

## Solution

Cylinder with height$$(h)=10cm$$ and diameter$$(2r)=7cm$$
Hemispheres cut from the top and bottom
Total Surface Area $$=$$ Curved Surface Area of Cylinder $$+$$ Curved Surface Area of $$2$$ hemispheres
$$=$$ CSA of Cylinder $$+$$ Total Surface Area of a Sphere
CSA of Cylinder $$= 2πrh$$ where $$r$$is the radius of the cylinder $$h$$is the height of the cylinder
TSA of Sphere $$4\pi {r}^{2}$$ where $$r$$ is the radius of the sphere
Total Surface Area of the article  $$=2\pi rh+4\pi {r}^{2}$$
$$=2\pi (3\mathrm{\ldotp }5)(10)+4\pi (3\mathrm{\ldotp }5{)}^{2}$$
$$=70\pi +49\pi$$
$$119\pi$$
$$=119\left(\dfrac{22}{7} \right)$$
$$=17\times 22$$
$$=374sq\ldotp m$$