Question

the volume of a cylindrical vessel; is 308 and its base area is 38.5 find its lsa
urgent please answer
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Answer 1

||✪✪ QUESTION ✪✪||

the volume of a cylindrical vessel; is 308 and its base area is 38.5 find its TSA ?

|| ★★ FORMULA USED ★★ ||

→ Volume of cylinder = πr²h

→ Base Area of cylinder is = πr²

→ TSA of cylinder = 2πr(h+r)

|| ✰✰ ANSWER ✰✰ ||

Putting values in formula we get,

➳ πr² = 38.5

➳ (22/7) * r² = 38.5

➳ r² = (38.5*7)/22

➳ r² = 12.25

Square root both sides now, we get,

➳ r = 3.5 cm. ------------ Equation (1) .

_______________________

now , volume is given 308cm³

➺ π * r² * h = 308

putting value of r from Equation (1) , we get,

➺ (22/7) * (3.5)² * h = 308

➺ h = ( 308 * 7 ) / (3.5*3.5*22)

➺ h = 8cm. ----------- Equation (2) .

___________________

Now, putting both Values of Equation (1) and (2) in TSA formula we get,

☞ TSA = 2πr(h+r)

☞ TSA = 2 * (22/7) * 3.5 * (8 + 3.5)

☞ TSA = 2 * 22 * (0.5) * 11.5

☞ TSA = 22 * 11.5

☞ TSA = 253 cm².

Hence, Total surface area of required cylinder is 253cm².

Answer 2

$\huge\tt{Answer:}$

Question:

✳ The volume of a cylinder vessel is 308 and it's base area is 38.5, Find it's TSA.

Solution:

Given:

✳ The volume of a cylinder vessel = 308.

✳ The base area of cylinder = 38.5

Find:

✳ Find it's TSA [Total surface area].

Formulas used to solve this question:

✳ Volume = πr² h

✳ Base area = πr²

✳ Total surface area = 2πr (h + r)

Adding values to the above formulas:

$\rightarrow π \:r {}^{2} = 38.5 \\ \rightarrow ( \frac{22}{7} ) \times r {}^{2} = 38.5 \\ \rightarrow r {}^{2} = ( \frac{38.5 \times 7}{22} ) \\ \rightarrow r {}^{2} = 12.25$

Squaring both the sides:

→ r = 3.5 cm _[ Equation-(1) ]

→ Volume = 308 cm³ { π × r² × h = 308 }

Adding value of (r) - Radius for [Equation-(1)]:

$\rightarrow ( \frac{22}{7} ) \times (3.5) {}^{2} \times h = 308 \\ \rightarrow h = \frac{(308 \times 7)}{(3.5 \times 3.5 \times 22)}$

→ h = 8cm _[ Equation-(2) ]

Adding values to Eq(1) and Eq(2) in total surface area using formula:

$\rightarrow TSA = 2 \: π \: r(h + r) \\ \rightarrow TSA = 2 \times ( \frac{22}{7} ) \times (3 .5) \times (8 + 3.5) \\ \rightarrow TSA = 2 \times 22 \times (0.5) \times 11.5 \\ \rightarrow TSA = 2 = 22 \times 11.5 \\ \rightarrow TSA = 253 \: cm {}^{3}$

Therefore, TSA of cylinder = 253 cm²

Also refer the attachment ;)