Multiple choice

A solid toy is in the form of a right circular cylinder with a hemispherical shape of one end and a cone at the other end. Then common diameter is $4.2 cm$ and the heights of the cyndrical and conical portions are $12 cm$ and $7 cm$, respectively. Find the volume of the solid. (Take $\pi$ = 22/7)

  1. $218.02\, cm^{3}$
  2. $178.66\, cm^{3}$
  3. $158.66\, cm^{3}$
  4. $138.66\, cm^{3}$
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A Correct answer
Explanation

The radius is 2.1 cm. Add the volumes of the cylinder, hemisphere, and cone: pi(2.1)^2(12) + (2/3)pi(2.1)^3 + (1/3)pi(2.1)^2(7), using pi = 22/7. This gives approximately 218.02 cm^3.

AI explanation

The common diameter is 4.2 cm, making the radius 2.1 cm. Using the respective volume formulas, the cylinder volume is π(2.1)^2(12) = 166.32 cm^3, the cone volume is (1/3)π(2.1)^2(7) = 32.34 cm^3, and the hemisphere volume is (2/3)π(2.1)^3 = 19.404 cm^3. Adding these three volumes gives 166.32 + 32.34 + 19.404 = 218.064 cm^3. Rounding to two decimal places gives the volume of the solid as 218.02 cm^3.

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