Question

a decorative block which is made of solid s - a cube and a hemisphere . the base of the block is acube with edge 5 cm , and the hemisphere fixed on the top has a diameter 4.2 cm . find the total volume and the total surface area of the block

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$    

${\boxed{\sf\:{ Firstly\:we\; have\;the\;information\;of\;cubical\;portion }}}$

Edge = 5 cm

Also,

${\boxed{\sf\:{ We\; have\;the\;information\;of\;hemispherical\;portion }}}$

Diameter = 4.2 cm

Hence,

Radius(r)

${\implies\dfrac{4.2}{2}}$          

= 2.1 cm

Using Formula we have :-

TSA of the cube

= 6 × (Edge)²

= 6 × (5)²

= 6 × 25

= 150 cm²

Hence,

TSA =  TSA of the cube + Area of base of hemisphere + CSA of hemisphere

TSA = 150 - πr² + 2πr²

TSA = 150 + πr²

${\implies 150+\dfrac{22}{7}\times 2.1\times 2.1}$    

     

= 150 + 13.86  

= 163.86 cm²

Answer 2

Total surface area of the block =

= TSA of the cube + CSA of the hemisphere - Base area of the hemisphere

= $\sf\red{6 {(side)}^{2} + 2\pi {r}^{2} - \pi {r}^{2}}$

= $\sf\red{6 \times ( {5cm)}^{2} + \pi {r}^{2} }$

= $\sf\red{150 {cm}^{2} + \frac{22}{7} \times 2.1 \times 2.1 {cm}^{2}}$

= $\sf\red{(150 + 13.86) {cm}^{2} }$

= $\sf\red{163.86 {cm}^{2}}$