Q) The inner and outer radii of a hollow cylinder surmounted on a hollow hemisphere of same radii are 3 cm and 4 cm respectively. If height of the cylinder is 14 cm, then find its total surface area (inner and outer).
Ans: Let’s draw a diagram to better understand the question:
Here, in this question, it is given that:
Outer radii (of sphere and cylinder), R1 = 4 cm
Inner radii (of sphere and cylinder), R2 = 3 cm
Height of cylinder, H = 14 cm
Total surface area = Outer Surface Area of Cylinder + Outer Surface Area of Hemisphere + Surface Area of Circular Ring at the top + Inner Surface Area of Cylinder + Inner Surface Area of Hemisphere
= ![2 \pi (R_1) H + 2 \pi (R_1)^2 + \pi [ (R_1)^2 - (R_2)^2 ] + 2 \pi (R_2) H + 2 \pi (R_2)^2](https://www.saplingacademy.in/wp-content/ql-cache/quicklatex.com-3acf5e4b1f5d602acb06b90a45770b08_l3.png "Rendered by QuickLaTeX.com")
= ![2 \pi (R_1) [H + R_1 ] + \pi [ (R_1)^2 - (R_2)^2 ] + 2 \pi (R_2) [ H + R_2 ]](https://www.saplingacademy.in/wp-content/ql-cache/quicklatex.com-340bb6be62b46ca7c2f21b1bb46826bc_l3.png "Rendered by QuickLaTeX.com")
= ![2 \pi (4)[ (14 + 4 ] + \pi [ (4)^2 - (3)^2 ] + 2 \pi (3) [ 14 + 3 ]](https://www.saplingacademy.in/wp-content/ql-cache/quicklatex.com-a78331b1b9a592af9dbfe9fa4b8464ba_l3.png "Rendered by QuickLaTeX.com")
= 
= 
= 253 x 
= 
= 795.14 cm2
Therefore, the total surface area (inner and outer) of the shape is 795.14 cm2
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