A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cy

Explanation

Radius of the conical part, r= 5/2 cm.
Height of the conical part, h= 6 cm
Radius of the cylindrical part, `R = 3/2 cm`
Height of cylindrical part , H =(26 -6) cm
Slant height of the conical part,
`l=sqrt(r^2+h^2)=sqrt((5/2)^2+6^2)cm`
`=sqrt(25/4+36)cm =sqrt(169/4 )cm = 13/2 cm`
Area to be painted orange
= curved suface area of the cone + base area of the cone - base area of the cylinder
`pirl + pi r^2 - pi R^2=pi (rl + r^2 - R^2)`
`=[3.14 xx(5/2xx13/2+5/2xx5/2-3/2xx3/2)]cm^2`
`=[3.14 xx (65 /4 +25/4-9/4)]cm^2=(3.14 xx 81 /4)cm^2`
`=(3.14 xx 20.25)cm^2 = 63.585 cm^2`
Area to the painted yellow
= curved surface area of the cylinder + base area of the cylinder
`=2pi RH + pi R( 2H + R)`
`= [3.14 xx 3/2 xx( 2 xx 20 + 3/2)]cm^2`
`=(3.14 xx 3/2 xx 83/2)cm^2 =((781.86)/(4)) cm^2`
`=195.465 cm^2`
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