Question

The total and curved surface area of a solid cylinder is 180 cm2 and 108 T cm 2, respectively. If a hole of radius 3 cm made along the axis of the cylinder, what quantity of material is removed (in cm ³)?​

Answer 1

Step-by-step explanation:

Volume of a Cylinder of Radius "R" and height "h" =πR

2

h

Hence, volume of the given cylinder =π×R

2

×14=54πcm

3

R

2

=3.86

R=1.96 cm

Curved Surface Area of a Cylinder of Radius "R" and height "h" =2πRh

Hence, CSA of the given cylinder =2×π×1.96×14=54.88πsqcm

Answer 2

given a cylinder with CSA=180cm^2 and TSA=108cm^2 and a hole of 3cm radius made along axis. Find the volume of removed material

Explanation:

1. let the radius of the solid cylinder be $r$ and height of the cylinder be $h$ then we have , $CSA=2\pi rh = 108cm^{2}$                                                                             $TSA=CSA+ 2(area\ of\ base\ circle)\\TSA = 2\pi rh + 2\pi r^{2}$                                                                    
2. as given $CSA=108cm^2$ and $TSA=180cm^2$ we get,                                                  $180=108+2\pi r^2\\r=\sqrt{\frac{180-108}{2\pi } } \\r=\frac{6} {\sqrt{\pi } }$          
3. putting this value of $r$ in formula of $CSA$ we get ,                                                   $2\pi rh=108\\2\pi \frac{6}{\sqrt{\pi } } h=108\\h=5\ cm(approx.)$        
4. for the quantity of material removed we need to find the volume of cut out cylinder. the radius of removed cylinder $r_1=3\ cm$   and   $h_1=5\ cm$         then we have , $V_{cylinder}= \pi r_1^{2}h_1\\V_{cylinder}= \pi (9)(5)\\V_{cylinder}= 141.4\ cm^3(approx.)$  
5. Quantity of material removed is approximately  $141.4\ cm^3$ .