Question

from a solid cylinder of height 2.8 cm and diameter 4.2cm a conical cavity of the same height and same diameter is hollowed out find the total surface area of the remaining solid.

Answer 1

The total surface area of remaining solid is 73.92 centimeters ²


Please refer the above photograph for the used process.

Hope this will be helping you!


KEY POINTS TO REMEMBER :-

☸️ Surface area of cylinder :-

$csa = 2\pi \: rh \\ \\ tsa = 2\pi \: r(r + h)$

☸️ Surface area of cone :-

$csa = \pi \: rl \\ \\ tsa = \pi \: r(r + l)$

☸️ Area of circle :-
$\pi \: {r}^{2}$

☸️ CSA = Curved surface area

☸️ TSA = Total surface area

Thanks!

Answer 2

⭐⭐⭐⭐Answer ⭐⭐⭐⭐⭐
For solid cylinder:-
Diameter=4.2 cm
then,Radius=2.1 cm
Height=2.8 cm
If l is the slant height of the cylinder.
Then,
$l = \sqrt{r {}^{2} + h {}^{2} } \\ = \sqrt{(2.1) {}^{2} (2.8) {}^{2} }$
Now, Total surface area of the remaining solid=
C. S. A. of the cylinder+ Area of the base of
the cylinder+ C.S.A. of the cone.
$2 \times 22 \div 7 \times 2.1 \times 2.8 + 22 \div 7 \times (2.1) {}^{2} + 22 \div 7 \times 2.1 \times \sqrt{(2.8) {}^{2} + (2.1) {}^{2} }$
Then,
=36.96+3.14×4.4+3.14×2.1×7.21
=36.96+13.81+47.54
=98.3 cm^2
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐