Question

A solid wooden toy is in the from of a hemisphere surmounted by a cone of same radius.the radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 5/6 cm3 find the height of the toy also find the cost of painting the hemisphere part of the toy at the rate of Rs.10 per cm2 [Use π = 22/7]

Answer 1

Answer:

Answer

r = radius of hemisphere and cone = 3.5 cm ; h = height of cone

Volume, Vtotal=Vcone+Vhemisphere=31πr2h+32πr3 =166.83cm3

⇒πr2(h+2r)=500.5cm3

⇒h+2(3.5)=π×3.52500.5

Hence h=13−7=6cm

Height of toy =h+r=6+3.5=9.5cm

Surface area of hemisphere  =2π(3.5)2=77cm2

Cost =Rs.770

Answer 2

Answer:

r = radius of hemisphere and cone = 3.5 cm ; h = height of cone

Volume, V

total

=V

cone

+V

hemisphere

=

3

1

πr

2

h+

3

2

πr

3

=166.83cm

3

⇒πr

2

(h+2r)=500.5cm

3

⇒h+2(3.5)=

π×3.5

2

500.5

Hence h=13−7=6cm

Height of toy =h+r=6+3.5=9.5cm

Surface area of hemisphere =2π(3.5)

2

=77cm

2

Cost =Rs.770