Question

Find the thickness of a hollow metallic cylinder whose outer radius, height and total surface area are 5 cm, 10 cm and 572 cm², respectively.​

Answer 1

Step-by-step explanation:

As per given picture External radius =R=8 cm

Internal radius =r (let)

Height =10 cm

Total surface area = 338πcm2

But Total surface area = Area of external cylinder (curved surface area)

+ Area of internal cylinder (curved surface area) + Twice Area of base (ring

2πR+2πr+2π(R2−r2)

⇒2π(Rh+rh+R2−r2)=338π

⇒(Rh+rh+R2−r2)=169

⇒(10×8)+(10×r)+(8)2−r2=169

⇒80+10r+64−r2=169

⇒−r2+10r−25=0

⇒r2−10r+25=0

⇒(r−5)2=0

⇒r=5

So, thickness of metal =R−r=(8−5) cm =3 cm.