Question

Find the volume , lateral ( curved ) surface area and total surface area of the cylinder whose dimensions are radius of base = 7 cm and height= 25cm​

Answer 1

Given -

• Radius of base = 7cm

• Height = 25cm

To find -

• Volume, curved surface area and total surface area of cylinder.

Solution -

Volume of cylinder = πr²h

where,

π = $\sf\dfrac{22}{7}$

r = radius

h = height

On substituting the values -

Volume = πr²h

Volume = $\sf\dfrac{22}{7}$ × (7cm)² × 25cm

Volume = $\dfrac{22}{ \cancel{7 \: _{1}} } \times { \cancel{49} \: \: }^{7} \times 25$

volume = 22 × 7cm × 25cm

$\longmapsto$ 3850cm³

Now,

Curved surface area of cylinder = 2πrh

where,

π = $\sf\dfrac{22}{7}$

r = radius

h = Height

On substituting the values -

CSA = 2πrh

CSA = 2 × $\sf\dfrac{22}{ \cancel7} \times \cancel{7} \times 25$

CSA = 2 × 22 × 25cm

$\longmapsto$ CSA = 1100cm

Now,

Total surface area of cylinder = 2πr(r + h)

where,

π = $\sf\dfrac{22}{7}$

r = radius

h = Height

On substituting the values -

TSA = 2πr(r + h)

TSA = 2 × $\sf\dfrac{22}{ \cancel7} \times \cancel{7}$ (7 + 25)

TSA = 2 × 22(32)cm

TSA = 44 × 32cm

$\longmapsto$ 1408cm³

$\therefore$ The volume, CSA and TSA of cylinder are 3850cm³ , 1100cm and 1408cm³

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Answer 2

$volume \: of \: cylinder \: - - \pi {r}^{2} h \: \\ - - \frac{22}{7} \times ({7}^{2} ) \times 25 \\ - - \frac{22}{7} \times 49 \times 25 \\ - - 22 \times 7 \times 25 \\ - - 3850 {cm}^{3} \\ \\ lateral \:curved \: surface \: area - - 2\pi rh \: \\ - - 2 \times \frac{22}{7} \times 7 \times 25 \\ - - 2 \times 22 \times 25 \\ - - 44 \times 25 \\ - - 1100 \\ \\ total \: surface \: area - - 2\pi r(r + h) \\ - - 2 \times \frac{22}{7} \times 7 \times (7 + 25) \\ - - 2 \times 22 \times 32 \\ - - 1408 \\ \\ hope \: it \: helps \: u \:$

gudu evening