A cylinder of height 4m and base radius 1m is surmounted by a conical top of slant height 2.8m. (i) Calculate the curved surface area of cylindrical portion? (ii) Find the height of conical part? (iii) Determine the curved surface area of conical part? Find the base area of cylinder? (v) Find the total surface area of combination?
Answers
Answer:
Sol. Volume of each cube = 64 cm3
∴ Total volume of the two cubes = 2 × 64 cm3
= 128 cm3
Let the edge of each cube = x
∴ x3 = 64 = 43
∴ x = 4 cm
Now, Length of the resulting cuboid l = 2x cm
Breadth of the resulting cuboid b = x cm
Height of the resulting cuboid h = x cm
∴ Surface area of the cuboid = 2 (lb + bh + hl) = 2[(2x . x) + (x . x) + (x . 2x)]
= 2[(2 × 4 × 4) + (4 × 4) + (4 × 2 × 4)] cm2
= 2 [32 + 16 + 32] cm2 = 2[80] cm2 = 160 cm2.
Given: h=4m
r=1m
l=2.8m
solution:
(i) curved surface area of a cylindrical portion
=2πrh
=2×22/7×1×4
=2×22×4/7
=176/7
=25.14
(ii)