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प्रश्न
A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2. The cone is placed upon the cylinder. The volume of the solid figure so formed is 500 cm3. Find the total height of the figure.
उत्तर
Given,
Height of the cylinder (h) = 3 cm
Area of the base of cylinder = 100 cm2
Volume of the solid figure = 500 cm3
A cylinder and a cone have equal bases.
∴ They have equal radii.
Radius of cylinder = Radius of cone = Area of base = 100 cm2
∴ πr2 = 100 ...(i)
Let the height of the cone be H cm.
Volume of the solid figure = Volume of the cylinder + Volume of the cone
∴ 500 = πr2h + `1/3`πr2H
∴ 500 = πr2 `("h" + "H"/3)`
∴ 500 = 100 `(3 + "H"/3)` ...[From (i)]
∴ `3 + "H"/3 = 500/100`
∴ `3 + "H"/3 = 5`
∴ `"H"/3 = 5 - 3`
∴ `"H"/3 = 2`
∴ H = 2 × 3
∴ H = 6 cm
∴ Height of conical part (H) = 6 cm
Total height of the figure = h + H = 3 + 6 = 9 cm
Thus, the total height of the figure is 9 cm.
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