Question

If the total surface area is 1232, and the ratio of total surface area and curved surface area of a cylinder is 2:1, find the radius and height of the cylinder.
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Answer 1

Answer:

Curved surface area of cylinder

$2\pi \: rh = \frac{1232}{2} = 616$

Total surface area of cylinder

$2\pi \: rh + 2\pi \: {r}^{2} = 1232$

So,

$2\pi \: rh = 2\pi {r}^{2} \\ rh = {r}^{2} \\ r = h \\ \\ \frac{r}{h} = \frac{1}{1}$

Answer 2

$\underline\red{\bold{ANSWERE}}$

• The height and radius of cylinder= 9.8 cm

$\underline\red{\bold{EXPLANATION}}$

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$\underline\red{\bold{GIVEN}}$

• The total surface area of a cylinder = 1232 cm2

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• The ratio of total surface area and curved surface area of a cylinder is 2:1

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$\underline\green{\bold{FORMULA}}$

• The total Surface area of cylinder =

$2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi \: r(r + h)$

• The surface area of curved of cylinder =

$2\pi \: rh$

where,

h = height of cylinder

r = radius

$\underline\red{\bold{SOLUTION}}$

According to this question

The ratio of total surface area and curved surface area of a cylinder is 2:1

$\frac{2\pi \: r(r + h)}{2\pi \: rh} = \frac{2}{1} \\ = > r + h = 2h \\ = > r = h$

The total surface area of a cylinder = 1232 cm2

$2\pi \: r(r + h) = 1232 \\ = > 2\pi \: r(r + r) = 1232 \\ = > 4\pi {r}^{2} = 1232 \\ = > {r}^{2} = \frac{1232}{4\pi} = 98 \\ = > r = 9.8 \: cm$

so. r = h = 9.8 cm

$\blue{\texttt{your answer}}$

so the height and radius of cylinder= 9.8 cm