Volumes Practice Test 3

Here, $\frac{\mathit{h}}{4}$ = 2r
∴ h = 8r
Since, 8r + r + r = 35
∴ r = $\frac{35}{10}$ = 3.5 cm and also, h = 8 × 3.5 = 28 cm
Volume of whole solid = $\mathit{\pi }{\mathit{r}}^2\mathit{h}+2\times \frac{2}{3}\mathit{\pi }{\mathit{r}}^3$
= $\frac{22}{7}\times {\left(3.5\right)}^2\left[28+\frac{4}{3}\times 3.5\right]$
= $38.5\times \frac{98}{3}$
= $\frac{3773}{3}$ = 1257.67 $\mathit{c}{\mathit{m}}^3$
Total surface area of the solid = $2\mathit{\pi }\mathit{r}\mathit{h}+2\times 2\mathit{\pi }{\mathit{r}}^2$
= 2πr (h + 2r)
= $2\times \frac{22}{7}\times 3.5$ (28 + 2 × 3.5)
= 22 × 35 = 770 $\mathit{c}{\mathit{m}}^2$