Question

11. A cylindrical pillar 70 cm in diameter and 4 m high is to be cemented all around the curved
surface. Find the cost of cementing it at the rate of 5 32 per m2.
​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Diameter of a cylindrical pillar

✭ Height of the pillar is 4 m

✭ Cost of cementing is 32 per m²

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The cost of cementing?

$\displaystyle\large\underline{\sf\gray{Solution}}$

Curved surface area of a cylinder is given by,

$\displaystyle \underline{\boxed{\sf CSA_{Cylinder} = 2\pi rh}}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

Given that the diameter of the cylinder is 70 cm, then it's radius will be,

$\displaystyle\sf :\implies Radius = \dfrac{Diameter}{2}$

$\displaystyle\sf :\implies Radius = \dfrac{70}{2}$

$\displaystyle\sf :\implies\green{Radius = 35 \ cm}$

Also on converting height to cm,

$\displaystyle\sf :\implies 1 \ m = 100 \ cm$

$\displaystyle\sf :\implies 4 \ m = 4\times 100$

$\displaystyle\sf :\implies \green{Height = 400 \ cm}$

So now the CSA of the cylinder will be,

$\displaystyle\underline{\boxed{\sf CSA_{Cylinder} = 2\pi rh}}$

• R = Radius = 35 cm
• H = Height = 400 cm

Substituting the values,

$\displaystyle\sf\twoheadrightarrow CSA = 2\pi rh$

$\displaystyle\sf\twoheadrightarrow CSA = 2\times \dfrac{22}{7} \times 35\times 400$

$\displaystyle\sf\twoheadrightarrow CSA = 2\times 22\times 5\times 400$

$\displaystyle\sf\twoheadrightarrow CSA = 88000 \ cm^2$

$\displaystyle\sf\twoheadrightarrow CSA = \dfrac{88000}{100}$

$\displaystyle\sf\twoheadrightarrow\orange{CSA = 880 \ m^2}$

Now the cost of cementing at ₹32 per m² is,

$\displaystyle\dashrightarrow \underline{\boxed{\sf Cost = Area \times 32}}$

$\displaystyle\sf\dashrightarrow Cost = 880 \times 32$

$\displaystyle\sf\dashrightarrow\pink{Cost = Rs \ 28160}$

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}} </p><p>$

$\green{\tt{\therefore{Radius\:of\:cylinder=5\:m}}}$$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}} </p><p></p><p>$

$\begin{gathered}\green{\underline \bold{Given:}} \\ \tt: \implies Height \: of \: cylinder = 21 \: m \\ \\ \tt: \implies Cost \: of \: decorating \:c.s.a = 72930 \: rupees \\ \\ \tt: \implies Cost \: of \: decorating \: 1 \: {m}^{2} = 110.5 \: rupees \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Radius \: of \: cylinder = ?\end{gathered} </p><p></p><p>$

• According to given question :

$\begin{gathered}\bold{As \: we \: know \: that} \\ \tt: \implies C.S.A \: of \: cylinder = \frac{cost \: of \: decorating \: C.S.A}{ost \: of \: decorating \: 1 \: {m}^{2} } \\ \\ \tt: \implies C.S.A \: of \: cylinder = \frac{72930}{110.5} \\ \\ \tt: \implies C.S.A \: of \: cylinder = 660 \: {m}^{2} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies C.S.A \: of \: cylinder = 2\pi rh \\ \\ \tt: \implies 660 = 2 \times \frac{22}{7} \times r \times 21 \\ \\ \tt: \implies 660 = 2 \times 22 \times 3 \times r \\ \\ \tt: \implies r = \frac{660}{44 \times 3} \\ \\ \green{\tt: \implies r = 5 \: m} \\ \\ \green{\tt \therefore Radius \: of \: cylinder \: is \: 5 \: m}\end{gathered} </p><p>$