Question

From a solid cylinder of height 7 cm and base diameter 12cm,a conical cavity of same height and smae base diameter is hollowed out. Find the total surface area of the remaining solid upto two decimal places. [Take root 85 =9.2]

Answer 1

the TSA of the solid is 550.6285 cm2

Answer 2

Answer:

The area of remaining solid is 203.66 cm².

Step-by-step explanation:

It is given that the height and diameter of the cylinder and cone is same.

$h=7$

$d=12$

$r=\frac{d}{2}=\frac{12}{2}=6$

The total surface area of cylinder is

$A_1=2\pi r(r+h)$

$A_1=2(\frac{22}{7})(6)(7+6)=490.2857$

The total surface area of cylinder is 264 cm².

The area of cone is

$A_2=\pi r(r+\sqrt{h^2+r^2})$

$A_2=(\frac{22}{7}) (6)(6+\sqrt{7^2+6^2})$

$A_2=(\frac{22}{7}) (6)(6+\sqrt{85})$

$A_2=(\frac{22}{7}) (6)(6+9.2)$

$A_2=286.6286$

The area of remaining solid is

$A=A_1-A_2$

$A=490.2857-286.6286=203.6571\approx 203.66$

Therefore the area of remaining solid is 203.66 cm².