A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.

Explanation

Toy is shown in the figure
Radius of hemisphere= 3.5 cm
Totla height = 15.5 cm
Height of cone h =15.5-3.5 = 12 cm
Slant height of cone l = `sqrt(12^(2)+3.5^(2))=sqrt(144+12.25)`
`=sqrt(156.25)=12.5 cm`
Now total surface area of toy `= 2pir^(2)+pirl=pir(2r+1)`
`=(22)/(7)xx3.5(2xx3.5+12.5)`
`=11xx19.5=2145 cm^(2)`

Volume `=(2)/(3)pir^(3)+(1)/(3)pir^(2)h=(1)/(3)pir^(2)(2r+h)`
`=(1)/(3)xx(22)/(7)xx3.5xx3.5xx(2xx3.5xx+12)`
`=(1)/(3)xx11xx3.5xx19=243.83 cm^(3)`