Multiple choice

A solid toy is in the form of a right circular with hemispherical ends. The total height of the solid is 19 cm and diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. (Take $\pi = \dfrac{22}{7}$)

  1. Volume = $681.66\, cm^{3};\,$ Total Surface Area = $ 478\, cm^{2}$
  2. Volume = $681.66\, cm^{3};\,$ Total Surface Area = $ 418\, cm^{2}$
  3. Volume = $641.66\, cm^{3};\,$ Total Surface Area = $ 478\, cm^{2}$
  4. Volume = $641.66\, cm^{3};\,$ Total Surface Area = $ 418\, cm^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The radius is 3.5 cm and the cylindrical portion has height 19 - 7 = 12 cm. Adding the cylinder volume and the volume of a sphere of radius 3.5 gives 641.66 cm^3, while the exposed area is 418 cm^2.

AI explanation

The total height is 19 cm and the diameter is 7 cm, meaning the two hemispherical ends have a combined height of 7 cm and the cylinder has a height of 12 cm. Using the volume formulas, the cylinder volume is π(3.5)^2(12) and the two hemispheres combine to a sphere volume of (4/3)π(3.5)^3, which totals to 641.66 cm^3. The total surface area is the curved surface area of the cylinder plus the surface area of the sphere, calculated as 2π(3.5)(12) + 4π(3.5)^2, resulting in 418 cm^2. The volume is 641.66 cm^3 and the total surface area is 418 cm^2.

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