Question

1) If the ratio of the curved surface areas of solid cone and a solid right circular cylinder having same base radii and same height is 5:8, then let us determine the ratio of their base radii and height.​

Answer 1

Let the same base radii be r units and same height be h units

Given:-

Ratio of CSAs of cone and cylinder with same height and base = 5 : 8

• CSA of cone = πrl sq.units
• CSA of cylinder = 2πrh sq.units

⇒ πrl / 2πrh = 5 / 8

⇒ l / 2h = 5 / 8

We know that

• l = √( r² + h² )

⇒ √( r² + h² ) / 2h = 5 / 8

Squaring on both sides

⇒ [ √(r² + h²) / 2h ]² = ( 5 / 8 )²

⇒ ( r² + h² ) / 4h² = 25 / 64

⇒ 64r² + 64h² = 100h²

⇒ 64r² = 100h² - 64h²

⇒ 64r² = 36h²

⇒ r² / h² = 36 / 64

⇒ ( r / h )² = 36 / 64

Taking square root on both sides

⇒ √( r / h )² = √( 36 / 64 )

⇒ r / h = 6 / 8

⇒ r / h = 3 / 4

⇒ r : h = 3 : 4

Answer 2

Answer:

$this \: is \: answer \: \\ please \: mark \: as \: brainlist$^_^^_^