hole has a
he volume
mounted on a
cylinder, as shown in the
A
6 cm
in conical
CBSE 2015)
14 c in
quantity
SE 2009)
counted
ume of
26 cm
by each of these colours. (Take 1 =
T = 2244
A wooden toy is in the shape of a cone
figure. The total height of the toy is 26 cm,
while the height of the conical part is 6 cm.
The diameter of the base of the conical
part is 5 cm and that of the cylindrical
part is 4 cm. The conical part and the
cylindrical part are respectively painted
red and white. Find the area to be painted
Answers
Answer:
A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 26cm, while the height of the conical part is 6cm. The base of the conical portion has a diameter of 5cm, while the base diameter of the cylindrical portion is 3cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take π=3.14)
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ANSWER
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
Curved surface area of cone =πrl
l=
6
2
+2.5
2
l=
36+6.25
l=
42.25
l=6.5 cm
Curved surface area of cone =3.14×2.5×6.5
=51.025 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(2.5)
2
=3.14×6.25
=19.625 cm
2
Curved surface area of cylinder =2πrh
=2×3.14×1.5×20
=188.4 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(1.5)
2
=7.065 cm
2
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
=51.025+19.625−7.0625
=63.59 cm
2
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
=188.4+7.065
=195.465 cm
2
Hence,
Area to be painted orange =63.59 cm
2
Area to be painted yellow =195.465 cm
2