Question

From a solid cylinder whose height is 4.2cm and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. ​

Answer 1

Dear Student,

★Answer:

The total surface area of the remaining solid is 37.4$cm^{2}$

Given:

➥Height (h) of the conical part = Height (h) of the cylindrical part = 4.2 cm

➥Diameter of the cylindrical part = 1.4 cm

★Step-by-step explanation:

Radius = $\frac{Diameter}{2}$

Radius(r) of the cylindrical part = 0.7 cm

➠ Slant height (l) of conical part = $\sqrt{r^{2} +h^{2} }$

                                                 = $\sqrt{ 0.7^{2} +4.2^{2}$

                                                 =  $\sqrt{ 0.49 +17.64$

                                                 =  $\sqrt{18.13$

                                                 =  4.2

➠Total surface area of the remaining solid = CSA of cylindrical part + CSA of conical part + Area of cylindrical base  

                                               = 2πrh + πrl + π$r^{2}$

                                               = 2 × $\frac{22}{7}$ × 4.2 + $\frac{22}{7}$  × 0.7 × 4.3 + $\frac{22}{7}$ × 0.7 × 0.7

                                               = 26.4 + 9.46 + 1.54

                                               = 37.4$cm^{2}$

➥Answer : The total surface area of the remaining solid is 37.4$cm^{2}$

                                               

Answer 2

Step-by-step explanation:

Dear Student,

★Answer:

The total surface area of the remaining solid is 37.4cm²

Given:

➥Height (h) of the conical part = Height (h) of the cylindrical part = 4.2 cm

➥Diameter of the cylindrical part = 1.4 cm

★Step-by-step explanation:

$Radius = \frac{Diameter}{2}$

Radius(r) of the cylindrical part = 0.7 cm

➠ Slant height (l) of conical part = $\sqrt{r^{2} +h^{2} }$

$= \sqrt{ 0.7^{2} +4.2^{2} }\\=\sqrt{ 0.49 +17.64}\\= \sqrt{18.13}\\= 4.2$

➠Total surface area of the remaining solid = CSA of cylindrical part + CSA of conical part + Area of cylindrical base

$= 2πrh + πrl + πr²$

$=2 \times \frac{22}{7} \times 4.2 + \frac{22}{7} \times 0.7 \times 4.3 + \frac{22}{7}\times0.7 \times 0.7$

= 26.4 + 9.46 + 1.54

= 37.4cm²

➥Answer : The total surface area of the remaining solid is 37.4cm²