A toy is in the form of a cone surmounted by a hemisphere whose radius is `3.5 cm` . If the total height of the toy is `15.5 cm` then find its total surface area and the Volume

Options

A. `214.5 cm^2 and 240 cm^3`
B. `240 cm^2 and 214.5 cm^3`
C. `214.5 cm^2 and 243.83 cm^3`
D. `243.83 cm^2 and 214.5 cm^3`

Answer

C

Explanation

Toy is shown in the figure
Radius of hemisphere= 3.5 cm
Total 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=214.5 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)`