Question

volume of cylinder is 448cm3 and height is 7cm , Find radius , TSA, LSA ​

Answer 1

$\mathfrak{\huge{\underline{Answer :}}}$

$\textbf{\underline{\underline{Given\:In\:The\:Question :}}}$

Volume = 448cm^3

Height = 7 cm

$\textbf{\underline{\underline{To\:Find\: Radius:}}}$

$\sf \: Volume = 448 {cm}^{3}$

$\sf \: \pi {r}^{2} h = 448 {cm}^{3}$

$\sf \dfrac{22}{ \cancel7} \times {r}^{2} \times \cancel7= 448 {cm}^{3}$

$\sf \: 22 {r}^{2} = 448 {cm}^{3}$

$\sf \: {r}^{2} = \dfrac{448}{22}$

$\sf {r}^{2} = \dfrac{224}{11}$

$\sf \: r = \sqrt{ \dfrac{224}{11} }$

$\huge{\boxed{\tt{4.51cm}}}$

$\textbf{\underline{\underline{To\:Find\: TSA:}}}$

Formula Of TSA =

$\sf \: 2\pi \: r(r + h)$

$\sf \: 2 \times \dfrac{22}{7} \times 4.51(4.51 + 7)$

$\sf{\dfrac{198.44}{7}\:\times\:11.51}$

$\huge{\boxed{\tt{326.16 cm^2}}}$

$\textbf{\underline{\underline{To\:Find\: LSA:}}}$

$\sf \: 2\pi \: rh$

$\sf \: 2 \times \dfrac{22}{ \cancel7} \times 4.51 \times \cancel7$

$\huge{\boxed{\tt{198.44cm^2}}}$

Answer 2

Answer:

HERE YOU GO~

As we know,

volume of cylinder = 448cm^3

height of cylinder = 7cm

radius = ?

T.S.A = ?

L.S.A = ?

SOLUTION~

πr^2h = 448cm^3

22/7 × r^2 × 7 = 448cm^3

22r^2 = 448cm^3

r^2 = 448/22

r^2 = 20.36

r = √20.36

THEREFORE radius = 4.512 cm.

NOW,

L.S.A = 2πrh

= 2×22/7× 4.512× 7

= 44× 4.512

= 198.528 cm^2

T.S.A = 2πr(r+h)

= 2×22/7×4.512(4.512+7)

= 44/7×4.512×11.512

= 44×4.512×1.644

= 326.380 cm^2

HOPE IT HELPS YOU.

THANKS ........ ..