Mathematics 4024 · O Level · Surface area and volume
Surface area and volume — practice question
A cone is placed on top of a hemisphere to make a solid. The cone and the hemisphere each have radius $r$ cm. The total height of the solid is $10$ cm. The curved surface area of the hemisphere is $145\text{ cm}^2$.
(a(i))[3]
Show that $r = 4.80$, accurate to $2$ decimal places.
(a(ii))[4]
Calculate the volume occupied by the solid.
(a(iii))[4]
Calculate the cone's curved surface area.
(b)[4]
Sector $A$ has angle $x$ and radius $y$. Sector $B$ has an angle $20\%$ smaller than $x$ and a radius $20\%$ longer than $y$. Calculate the area of sector $B$ as a percentage of the area of sector $A$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Either $2\pi r^2=145$ or $4\pi r^2=290$.” …