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TSA = 231 cm² and CSA = 2 / 3 × TSA

Answer 1

→ Hey Mate,

→ Given Question:-

→   TSA = 231 cm² and CSA = 2 / 3 × TSA

→ Solution:-

→ TSA = 231cm² and CSA = 2/3 × TSA

→ TSA = 231cm² and CSA = 154 cm²

→ 2πrh + 2πr² = 231 cm² and 2πrh = 154cm²

→ 2πr² + 154 = 231 cm² and 2πrh = 154cm²

→ 2πr² = 77 and 2πrh = 154

→ 2 × 22 / 7 × r² = 77 and  

→ 2 × 22 / 7 × r × h = 154

→ r = 7 / 2 cm and 2 × 22 / 7 × 7 / 2 × h = 154

→ r = 7 / 2 cm and h = 7cm

→ ∴ v = πr²h = 22 / 7 × 49 / 4 × 7 cm³ = 269.5cm³

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Answer 2

Step-by-step explanation:

Let the radius of the cylinder be r and the height be h.

The curved surface area of the cylinder is given by

2πrh

Total surface area of the solid cylinder is given as the sum of the curved surface area and the areas of the base and the top:

2πr

2

+2πrh

Given that

2πrh=

3

2

(2πrh+2πr

2

)

⇒h=2r

Also, given that

2πr

2

+2πrh=231

i.e

2πr

2

+2πr.2r=231

6πr

2

=231

⇒r=

2π

77

Volume of the cylinder:

=πr

2

h

=πr

2

.2r=2πr

3

=2π(

2π

77

)

3/2

=77

2π

77

Hence, volume of the cylinder =77

2π

77

cm

3