Page 293 - Start Up Mathematics_8 (Non CCE)

Example 27: The ratio between the curved surface area and the total surface area of a right circular cylinder
is 2 : 3. Find the ratio between the height and radius of the cylinder.
Solution: Let the height of the cylinder be h and the radius be r.
Curved surface area = 2prh = h
+
Totalsurface area 2prh( + r) hr
h 2
Now, =
hr+ 3

fi 3h = 2(h + r) fi 3h = 2h + 2r fi 3h – 2h = 2r
h 2
fi h = 2r fi = or h : r = 2 : 1
r 1

Example 28: A rectangular sheet of aluminium foil is 44 cm long and 22 cm wide. A cylinder is made out
it by rolling the foil along its length. Find the total surface area of the cylinder.

Solution: Height of cylinder (h) = 22 cm
Let the radius of cylinder be r cm. 22 cm
Circumference of base of cylinder = 44 cm
( Length of rectangle becomes the circumference of base) 44 cm

22
fi 2pr = 44 fi 2 × × r = 44 r
7
744¥ h 22 cm
fi r = = 7 cm
222¥
Hence, radius of base (r) = 7 cm
22
\ Total surface area = 2pr(h + r) = 2 × × 7 × (22 + 7) cm 2
7
22
2
= 2 × × 7 × 29 cm = 1,276 cm 2
7
Example 29: An open cylindrical tank of depth 1.5 m and radius of base 70 cm is to be made from a metal
sheet. How many square metres of metal sheet is needed?
Solution: Height of cylinder (h) = 1.5 m, Radius of base (r) = 70 cm = 0.7 m

Since the cylinder is open from the top,
the area of metal sheet needed = CSA + Area of base

= 2prh + pr 2

22 22
= 2 × × 0.7 × 1.5 + × 0.7 × 0.7
7 7
2
= (6.6 + 1.54) m = 8.14 m 2
2
Hence, 8.14 m of metal sheet is required to make the cylindrical tank.
2
Example 30: The lateral surface area of a hollow cylinder is 4,224 cm . It is cut along its height and formed
into a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet. (NCERT)
Solution: Let the height of cylinder (h) = width of the sheet (b) = 33 cm and the radius of the base of
hollow cylinder be r cm.

285