On the top of a cubical box a pyramid is placed, base of the pyramid being the same as the top of the box. Height of the pyramid is twice the height of the box. The ratio of the volume of the combined body to that of the box is
Solution
Let base is square with side =$a$
So base area = $a^2$
Let also height= B
So height of pyramid $= 2B$
Volume of box= $a^2 B
So, volume of pyramid= $\dfrac{1}{3} \times$ area of base $\times$ height
$= \dfrac{1}{3} \times a^2 \times 2B$
So, according to question
Total volume of combined body
$a^2B + \dfrac{2a^2 B}{3} \Rightarrow \dfrac{5a^2B }{3}$
So, Ratio = $ \dfrac{5 a^2B}{3} : a^ 2B \Rightarrow \dfrac{5}{3}$