Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

An object is formed by taking a uniform solid hemisphere of radius $0.56\,\text{m}$ with centre $O$ and then removing from it a hemisphere of radius $0.28\,\text{m}$ with centre $O$. The diagram shows a cross-section of the object through $O$.
(i)[4]

Calculate the distance of the centre of mass of the object from $O$. [The volume of a hemisphere is $\frac{2}{3}\pi r^3$].

(ii)[3]

The object weighs $24\,\text{N}$. A uniform hemisphere $H$ of radius $0.28\,\text{m}$ is inserted into the hollow region of the object to produce a non-uniform hemisphere with centre $O$. The centre of mass of the non-uniform hemisphere is $0.15\,\text{m}$ from $O$. Calculate the weight of $H$.

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