Question

The radius and the height of a cylinder are in the ratio 7 : 3. If the volume of the cylinder is
12474 cm find the curved surface area and the total surface area of the cylinder.
please help me​

Answer 1

Answer:

Let r,h be radius & hight of cylinder 

   ⇒volume=πr2h,Total surface area (T.S.A)=2πr(h+r)

Given. hr=27⇒h=72r

Volume =πr2h=8316⇒πr2(72r)=8316

   ⇒r3=2×228316×7×7=2×2273×1188=73×33

    ⇒r=7×3=21cm⇒h=72×21=6cm

T.S.A=2πr=(h+r)=2×722×21(6+21)=44×3×27

                                                                           =3564cm2

Step-by-step explanation:

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Answer 2

Let,

• Radius is 7x cm
• Height is 3x cm

Volume of Cylinder

• $\boxed{\sf\green{V = π r²h}}$

Here ⭐ :

• Value of π is $\bf \frac{22}{7}$
• Volume of Cylinder is 12474 (given)
• r is Radius = 7x (given)
• h is Height = 3x (given)

Putting these values in given formula

$\longrightarrow \boxed{ \bf \: V = \pi \: rh} \\ \\ \rightarrow \sf \: 12474 = \frac{22}{7} (7x) {}^{2} \times 3x \\ \\ \rightarrow \sf 12474 = \frac{22}{ \cancel7} \times \cancel{ 49}x {}^{2} \times 3x \\ \\ \rightarrow \sf {x}^{3} = \frac{12474}{22 \times 7 \times 3} \\ \\ \rightarrow \sf {x}^{3} = \frac{ \cancel{81}}{ \cancel{3}} \\ \\ \rightarrow \sf {x}^{3} = 27 \\ \\ \rightarrow \sf \: x = \sqrt[3]{27} \\ \\ \rightarrow \sf \pink{\boxed{\bf \green{ x= 3}}}$

• Radius = 7x ⇒ 7 × 3 = 21 cm
• Height = 3x ⇒3 × 3 = 9 cm

Curved Surface area of Cylinder

• $\boxed{ \green{\sf 2π rh}}$

Here ⭐ :

• r is Radius = 21 cm
• Value of π = $\bf \frac{22}{7}$
• h is Height = 9cm

Putting these values in given formula

$\longrightarrow \boxed{ \sf2\pi \: rh} \\ \\ \rightarrow \sf2 \times \frac{22}{ \cancel{7}} \times \cancel{ 21 }\times 9 \\ \\ \rightarrow \sf44 \times 27 \\ \\ : \implies \red{ \boxed{ \green{ \bf1188 \sf \: cm {}^{2} }}}$

Total Surface Area of Cylinder

• $\boxed{\green{\sf 2π r (h + r) }}$

Here ⭐:

• r is Radius = 21 cm
• Value of π = $\bf \frac{22}{7}$
• h is Height = 9cm

Putting these values in given formula

$\longrightarrow \boxed{ \sf \: 2\pi \: r \: (h + r)} \\ \\ \rightarrow \sf \: 2 \times \frac{22}{ \cancel7} \times \cancel{ 21}(9 + 21) \\ \\ \rightarrow \sf2 \times 22 \times 3(30) \\ \\ \rightarrow \sf44 \times 90 \\ \\ : \implies \sf \red{ \boxed{ \green{\bf \: 3960 \sf \: cm {}^{2} \:}}}$

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