Question

The following figure shows a model which is the combination of a cone and cylinder.total length of the model is 52 cm, the length of conical portion is 12m, the base of the cylindrical . portion has diameter of io cm and the base of the cylindrical portion 1 of diameter 6 cm. if the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the model with each of these colours.​

Answer 1

Given: Total length of the model is 52 cm

Length of conical portion is 12  cm

Solution:

Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder.

Radius of the cylinder is D/2= 3 cm

Radius of the cone is D/2= 5 cm

Slant height=l= $\sqrt{h^{2}+ r^{2} }$

                      =$\sqrt{12^{2} +5^{2} }$

                     =$\sqrt{144+25}$

                      =$\sqrt{169}$

                      = 13 cm

Curved surface area of cone =πrl

                                                = 3.14X5X13

                                                = 204.1 $cm^{2}$

Bottom area of cone = Area of circle

                               =π$r^{2}$

                               = 3.14X5X5

                               = 78.5 $cm^{2}$

Bottom area of cylinder = Area of circle

                                    =π$r^{2}$

                                    = 3.14X3X3

                                    = 28.26 $cm^{2}$

Area to be painted orange= 204.1+78.5-28.26 $cm^{2}$

                                           = 254.34 $cm^{2}$

Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder

Curved surface area of the cylinder=2πrh

                                                           = 2X3.14X3X40

                                                           = 753.6 $cm^{2}$

Area to be painted yellow= 753.6+28.26 $cm^{2}$

                                          = 781.86 $cm^{2}$

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