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A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket 

[Use \pi = 3.14].

Answers (1)

Diameter of cylinder = 6 cm

            Radius = 3 cm

            Height = 12 cm

            \text{ Surface are} =2 \pi r h = 2\pi \times 3 \times 12 = 72 \pi cm^2

            Similarly radius of circle = 3 cm

          \text{ Area} =\pi r^2=\pi 3 \times 3 = 9 \pi cm^2

            Slant height of cone (l)=5cm

            Radius = 3 cm

\text{ Surface area}=\pi r l =\pi \times 5 \times 3 = 15\pi cm^2

            Total surface area = area of cylinder + area of circle + area of the cone

                        =72\pi + 9 \pi + 15 \pi

                        =96\pi

                        =96\times 3.14=301.7 cm^2

            Slant height (l) = 5cm

            We know that,

h^2+r^2=l^2

 h^2+3^2=5^2

 \\h^2= 25 -9 \\ h^2=16 \\\ h = 4                 

\text{ Volume of cylinder= }\pi r^2 h \\ = \pi \times 3 \times 3 \times 12 = 108 \pi cm^3                  

 \\\text{ Volume of cone}=\frac{1}{3}\pi r^2 h \\ = \frac {1}{3} \pi \times 3 \times 3 \times 12 = 12 \pi cm^3                                 

\text{ Volume of rocket }=180 \pi + 12 \pi

                        =120 \pi

                        =120 \times 3.14 =377.14 cm^3

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