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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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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 
Question: 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

Answer

\(374\ m^2\)
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Solution

Solution for 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
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  \(=2\pi rh+4\pi {r}^{2}\)
\(=2\pi (3\mathrm{\ldotp }5)(10)+4\pi (3\mathrm{\ldotp }5{)}^{2}\)
\(=70\pi +49\pi\)
\(119\pi\)
\(=119\left(\dfrac{22}{7} \right)\)
\(=17\times 22\)
\(=374sq\ldotp m\)
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