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Question
Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.
Solution
Radius of the cone = Radius of the cylinder
r = `3/2` cm
Height of the cone (H) = 2 cm
Height of the cylinder (h) = 12 – (2 + 2) cm = 8 cm
Volume of the model = Volume of the cylinder + Volume of 2 cones
= `pi"r"^2"h" + 2 xx 1/3 pi"r"^2"H"`
= `pi"r"^2("h" + 2/3"H")"cm"^3`
= `22/7 xx 3/2 xx 3/2 (8 + 2/3 xx 2)"cm"^3`
= `(11 xx 3 xx 3)/(7 xx 2) ((24 + 4)/3)"cm"^3`
= `(11 xx 3 xx 3 xx 28)/(7 xx 2 xx 3)"cm"^3`
= `(11 xx 3 xx 4)/2 "cm"^3`
= 11 × 3 × 2 cm3
= 66 cm3
Volume of the model = 66 cm3
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