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  •  In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4·2 cm. Find the tota

 In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4·2 cm. Find

  1. the total surface area of the block.
  2. the volume of the block formed. \left(\text{Take }\pi=\frac{22}{7} \right )

 

 
 
 
 
 

Answers (1)

  1. \begin{align*}\text{Total surface are of block}& = \text{TSA of cube + CSA of hemisphere - Base area of hemisphere} \\ & = 6a^2 + 2\pi r^2 - \pi r^2 \\ & = 6a^2 + \pi r^2 \\ & = 6\times 6^2 + \frac{22}{7}\times 2.1\times 2.1 \\ & = 229.86 \ \text{cm}^2\end{align*}
  2.  

???????\begin{align*}\text{Volume of Block}& = a^3 + \frac{2}{3}\pi r^3 \\ & = 6^3 + \frac{2}{3}\times \frac{22}{7}\times (2.1)^3 \\ & = (216 + 19.40) \text{ cm}^3 \\ & = 235.40 \ \text{cm}^3\end{align*}

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