Sunita baked a cake for her daughter’s birthday. The cake is in the shape of a cylinder
with radius 7cm and height 9cm.
(a) The volume of the cake is:
(i) 256cm3
(ii) 1078cm3
(iii) 9702cm3
(iv) 1386cm3
(b) The area to be coated with icing, if all the surfaces except the base is to be coated, is:
(i) 550cm2
(ii) 440cm2
(iii) 320cm2
(iv) 580cm2
(c) The volume of the cone with the same radius and height is:
(i) 155cm3
(ii) 462cm3
(iii) 286cm3
(iv) 393cm3
(d) If the radius of the cake is halved and the height is doubled, then the volume of the new
cylinder is:
(i) doubled (ii) tripled (iii) halved (iv) increased by 1cm3
(e) The ratio of the volume of a cone to the volume of a cylinder of same radius and height
is:
(i) 1:2 (ii) 1:3 (iii) 1:4 (iv) 2:3
Answers
Answer:
a) iv
b) i
c)ii
d)iii
e)ii
Step-by-step explanation:
Given,
radius=7 cm and height=9 cm
a) volume of cylinder= π*r^2*h
=22/7*7*7*9
=1386 cm3
b)total surface area of cylinder=2*π*r(r+h)
=2*(22/7)*7*16
=704
the icing will be coated to all surfaces except base
here the base is circle so area of circle π*r^2
=(22/7)*49
=154
total surface area of cylinder-area of circle=704-154
=550 cm2
c)volume of cone is 1/3*π*r^2*h
= 1/3*(22/7)*49*9
=462 cm3
d) if radius is halved and the height is doubled
then r=7/2=>3.5 and h=2*9=>18
then the volume of the new cylinder is:π*r^2*h
=(22/7)*3.5*3.5*18
=693 cm3
volume of cylinder= π*r^2*h
=22/7*7*7*9
=1386 cm3
1386/2=693 cm3 (halved)
e) The ratio of the volume of a cone to the volume of a cylinder of same radius and height is:
volume of cone is 1/3*π*r^2*h
= 1/3*(22/7)*49*9
=462 cm3
volume of cylinder= π*r^2*h
=22/7*7*7*9
=1386 cm3
462/1386=1/3
1:3
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