### volume of right circular cylinder

Question Sample Titled 'volume of right circular cylinder'

A toy company is going to produce solid plastic blocks in the shape of right circular cylinder. There are two types available:

 Type ${A}$: Base radius ${R}$ $\text{cm}$ with height ${H}$ $\text{cm}$ Type ${B}$: Base radius ${r}$ $\text{cm}$ with height ${5}$ $\text{cm}$

It is given that the total volume of ${2}$ blocks of Type ${A}$ is equal to the total volume of ${18}$ blocks of Type ${B}$; and the base area of Type ${A}$ is ${9}$ times that of Type ${B}$.

 (a) Find (i) ${r}:{R}$, (ii) the height Type ${A}$.

  (5 marks) (b) The designer of the company claims that the shapes of Type ${A}$ and Type ${B}$ are similar. Do you agree? Explain your answer. (2 marks)

 (ai) $\dfrac{{\pi{r}^{{2}}}}{{\pi{R}^{{2}}}}$ $=\dfrac{{1}}{{9}}$ 1M ${\left(\dfrac{{r}}{{R}}\right)}^{{2}}$ $=\dfrac{{1}}{{9}}$ $\dfrac{{r}}{{R}}$ $=\dfrac{{1}}{{3}}$ ${r}:{R}$ $={1}:{3}$ 1A  (ii) ${2}\pi{R}^{{2}}{H}$ $={18}{\left(\pi{r}^{{2}}{\left({5}\right)}\right)}$ 1M ${H}$ $={45}{\left(\dfrac{{r}}{{R}}\right)}^{{2}}$ ${H}$ $={45}{\left(\dfrac{{1}}{{3}}\right)}^{{2}}$ 1M ${H}$ $={5}$ Thus, the height of Type ${A}$ is ${5}$ $\text{cm}$. 1A

 (b) Base radius of Type ${A}:$ Base radius of Type ${B}$ $={3}$ Height of Type ${A}:$ Height of Type ${B}$ $=\dfrac{{5}}{{5}}={1}$ ∵   These ratios are not equal. ∴   The shapes of Type ${A}$ and Type ${B}$ are not similar. 1M Thus, the claim is disagreed. 1A

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