Question

The radius of the two solids used to make the ladders is the same, i.e. 6 ft. What is the total volume used to make the two ladders?

• A. $828\pi$ ft${}^3$
• B. $628\pi$ ft${}^3$
• C. $540\pi$ ft${}^3$
• D. $880\pi$ ft${}^3$

Answer 1

The correct option is A $828\pi$ ft${}^3$

Using the Cavalieri's principle, we know that the 3-dimensional solids of the same height are equal in volume if the areas of their horinzontal cross-sections at every height h are equal.

So,
Total Volume of the ladder = Volume of sphere + Volume of cylinder

$=\frac{4}{3}\pi r^3+\pi r^{2}h$

$=\frac{4}{3}\times \pi \times 6^3+\pi \times 6^2\times 15$

$=288\pi +540\pi$

$=828\pi$ ft${}^3$