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In the given figure, the radius of the cone is same as its height equal to 2 cm each. The sum of the volumes of the whole body is :

  1. 8π cm3

  2. 16 cm3

  3. 32π cm3

  4. 32 cm3

In the given figure, the radius of the cone is same as its height equal to 2 cm each. The sum of the volumes of the whole body is : Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

Mensuration

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Answer

Given,

Radius of cone (r) = 2 cm

Height of cone (h) = 2 cm

From figure,

Radius of hemisphere = Radius of cone = 2 cm.

⇒ Volume of body = Volume of cone + Volume of hemisphere

⇒ Volume of body = 13πr2h+23πr3\dfrac{1}{3}πr^2h + \dfrac{2}{3}πr^3

=πr23(h+2r)=π×223×(2+2×2)=4π3×(2+4)=4π3×6=24π3=8π cm3.= \dfrac{πr^2}{3}(h + 2r) \\[1em] = \dfrac{π \times 2^2}{3} \times (2 + 2 × 2) \\[1em] = \dfrac{4π}{3} \times (2 + 4) \\[1em] = \dfrac{4π}{3} \times 6 \\[1em] = \dfrac{24π}{3} \\[1em] = 8π \text{ cm}^3.

Hence, Option 1 is the correct option.

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