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Question
A cylinder and a cone have equal bases. The height of the cylinder is 2 cm and the area of its base is 64 cm2. The cone is placed upon the cylinder volume of the solid figure so formed is 400 cm3. Find the total height of the figure.
Solution
The bases of a cone and a cylinder are equal.
∴ They have equal radii.
Let r be the radius.
Area of its base = 64 cm2
∴ πr2 = 64 cm2
And the height of cylinder h1 = 2 cm
Volume of solid figure = 400 cm3
∴ The volume of the solid figure = Volume of the cylindrical Part + Volume of the conical part
∴ `pir^2h_1 + 1/3 pir^2h_2` = 400
∴ `64 xx 2 + 1/3 xx 64 xx h_2` = 400 .......[From (i)]
∴ `128 + 64/3 xx h_2` = 400
∴ `64/3 h_2` = 400 – 128
∴ `64/3 xx h_2` = 272
∴ h2 = `(272 xx 3)/64`
h2 = 12.75 cm
Height of figure = h1 + h2 = 2 + 12.75 = 14.75 cm
Hence, the height of the figure = 14.75 cm
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