Question

The volume of a cylinder is 448 pi cm3 and height 7 cm. Find its lateral surface area and total surface aran.
​

Answer 1

Given:-

• The volume of a cylinder i= 448π cm³

• Height,h = 7 cm

To find out:-

Find the lateral surface area and total surface area.

Formula used:-

• Volume of cylinder = πr²h

• Lateral surface area of cylinder = 2πrh

• Total surface area = 2πr ( h + r )

Solution:'

We know that,

Volume of cylinder = 448π

⇒ π × r² × h = 448π

⇒ π × r² × 7 = 448π

⇒ r² = 448π/7π

⇒ r² = 64

⇒ r = √64

⇒ r = 8 cm

Now,

★ Lateral surface area of cylinder = 2πrh

= 2 × 22/7 × 8 × 7

= 44 × 8

= 352 cm²

★ Total surface area = 2πr ( h + r )

= 2 × 22/7 × 8 ( 7 + 8 )

= 44/7 × 8 × 15

= 5280/7

= 754.28 cm²

Hence,the lateral surface area of cylinder and Total surface area of cylinder are 352 cm² and 754.28 cm² respectively.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

The volume of a cylinder is 448 pi cm³ and height 7 cm. Find its lateral surface area and total surface aran...

_______________

${ \huge{ \bold{ \underline{ \underline{ \orange{Answer:-}}}}}}$

✒Given : -

• Volume of Cylinder = 448πcm³
• Height = 7cm

✒To Find : -

• Lateral Surface Area (L.H.S)
• Total Surface Area (T.S.A)

✒Using Formula : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \red{Volume\:of\:Cylinder=\pi{{r}^{2}h}}}}}}}}$

✒On Substituting Values : -

$\dashrightarrow\sf{{\cancel{\pi}}\times{r}^{2}\times{7}=448{\cancel{\pi}}}$

$\dashrightarrow\sf{{r}^{2}=\cancel\dfrac{448}{7}}$

$\dashrightarrow\sf{{r}^{2}=\sqrt{64}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \blue{r=8cm}}}}}}}$

✒Now ,

✒Using Formula : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \green{L.S.A\:od\:Cylinder=2\pi{rh}}}}}}}}$

✒On Substituting Values : -

$\dashrightarrow\sf{2\times\dfrac{22}{{\cancel{7}}}\times{8}\times{{\cancel{7}}}}$

$\dashrightarrow\sf{44\times{8}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \pink{352{cm}^{2}}}}}}}}$

✒Then ,

✒Using Formula : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \purple{T.S.A\:of\:Cylinder=2\pi{r}(h+r)}}}}}}}$

✒On Substituting Values : -

$\dashrightarrow\sf{2\times\dfrac{22}{7}\times{8}\:(h+r)}$

$\dashrightarrow\sf{\dfrac{44}{7}\times{8}\times{15}}$

$\dashrightarrow\sf{\cancel\dfrac{5280}{7}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \orange{754.28{cm}^{2}}}}}}}}$

Therefore , L.S.A of Cylinder is 352cm² and T.S.A of Cylinder is 754.28cm² ....