Answer:
Side of the cubical block \[(a)=10\text{ }cm\] Longest diagonal of the cubical block \[=a\sqrt{3}\] \[=10\sqrt{3}\,cm\] Since the cube is surmounted by a hemisphere, therefore the side of the cube should be equal to the diameter of the hemisphere. \[\because \] Diameter of the sphere \[=10\text{ }cm\] \[\therefore \] Radius of the sphere \[r=5\text{ }cm\] \[\left[ \because \,\,Radius=\frac{Diameter}{2} \right]\] Total surface area of solid = T.S.A. of the cube + C.S.A. of hemisphere\[-\]Inner cross-section area of hemisphere \[=6{{a}^{2}}+2\pi {{r}^{2}}-\pi r2\] \[=6{{a}^{2}}+\pi {{r}^{2}}\] \[=6{{(10)}^{2}}+3.14{{(5)}^{2}}\] \[[\because \,\,\pi =3.14]\] \[=600+25\times 3.14\] \[=600+78.5\] \[=678.5\,c{{m}^{2}}\] Cost of painting per square metre is Rs. 5 Total cost for painting \[=\frac{Rs.\,678.5}{100}\times 5\] \[=Rs.\,33.92\] Hence, total cost for painting will be \[Rs.\,33.92\].
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