(a)[3]
Show that $y = \dfrac{4R}{3}$.
(b)[4]
Find the cone volume in terms of $R$. Present your answer in its simplest form.
Mathematics 4024 · O Level · Surface area and volume
Surface area and volume — practice question
Volume of a cone $= \dfrac{1}{3}\pi r^2 h$, curved surface area of a cone $= \pi r l$. Surface area of a sphere $= 4\pi r^2$. A solid cone has radius $y\,\text{cm}$. The slant height of the cone is $25\%$ greater than its radius. A solid sphere has radius $R\,\text{cm}$. The sphere's surface area is the same as the cone's total surface area.