Multiple choice

A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm, respectively, and the height of the cylindrical part of the solid is 3.5 cm, the volume of the solid is equal to

  1. $\displaystyle 293\frac{1}{3}\, cm^{3}$
  2. $\displaystyle 293\frac{1}{5}\, cm^{3}$
  3. $\displaystyle 298\frac{1}{3}\, cm^{3}$
  4. $\displaystyle 298\frac{1}{5}\, cm^{3}$
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AI explanation

The total volume is the sum of the cylindrical and conical parts, found using the formulas πr^2h and (1/3)πr^2h. The cylinder volume is π(4)^2(3.5), yielding 56π cm^3. The cone volume is (1/3)π(4)^2(7), yielding approximately 37.33π cm^3. Summing these gives 93.33π, and using π = 22/7 results in 293.33 or 293 1/3 cm^3.

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