Question

If total Surface area of a cylinder is 40πcm² and radius is 4 cm find the height

Answer 1

Answer:

TSA of cylinder = 2πr(r+h)

40π=2π*4(4+h)

40π/8π=4+h

5=4+h

h= 5-4=1cm

Answer 2

$\bf\huge\blue{\underline{\underline{ Question : }}}$

If total Surface area of a cylinder is 40πcm² and radius is 4 cm, then find the height.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• $\tt\: Total\:Surface\:Area\:_{(Cylinder)} = 40 \pi cm^{2}$
• $\tt\: Radius\:_{(Cylinder)} = 4 cm.$

★ To find,

• $\tt\:Height_{(Cylinder)} = ? cm.$

★ Formula :

$\tt\red{:\leadsto Total\:Surface\:Area\:_{(Cylinder)} = 2 \pi r(r + h)}$

• Substitute the values.

$\bf\:\implies 2 \times \pi \times 4 (4 + h) = 40 \times \pi$

$\bf\:\implies 8 \times \pi (4 + h) = 40 \times \pi$

$\bf\:\implies (4 + h) = \cfrac{40 \times \pi}{8 \times \pi}$

$\bf\:\implies 4 + h = 5$

$\bf\:\implies h = 5 - 4$

$\bf\:\implies h = 1$

★ Verification,

• Substitute all the values in the formula.

$\bf\:\implies 2 \times \pi \times 4(4 + 1)$

$\bf\:\implies 8 \times \pi (5)$

$\bf\:\implies 40 \pi$

# Hence,it was verified.

$\underline{\boxed{\rm{\purple{\therefore Height\:_{(Cylinder)} = 1 \:cm. }}}}\:\orange{\bigstar}$

★ More information :

Formulae related to Cylinder :

➡ TSA :- 2πr(r + h)

➡ CSA :- πrh

➡ Volume :- πr²h

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