Question

a cylinder and the cone have equal height and equal radius of their base if their covered surface area are in the ratio of 8:5 show that the ratio of radius to height of each is 3:4​

Answer 1

Appropriate Question :

• a cylinder and the cone have equal height and equal radius of their base if their curved surface area are in the ratio of 8:5 show that the ratio of radius to height of each is 3:4.

Given :

• Radius of cylinder = Radius of cone
• Height of cylinder = Height of cone
• Their csa are in the ratio 8:5.

To Find :

• We need to show that their ratio of radius to height of each is 3:4.

Solution :

• CSA of cylinder = 2πrh
• CSA of cone = πrl
• Let the height and radius of cylinder be r and h respectively.
• Let the height, radius and slant height of the cone be h,r and l respectively.

★ According to Question now :

→ CSA of cylinder ÷ CSA of cone = 8 ÷ 5

→ 2πrh ÷ πrl = 8 ÷ 5

Cancelling the π and r from both numerator and denominator we get :

→ 2h ÷ l = 8 ÷ 5

→ 2h ÷ √(r)² + (h)² = 8 ÷ 5

Squaring both the sides we get :

→ [2h ÷ √(r)² + (h)²]² = [8 ÷ 5]²

→ 4h² ÷ r² + h² = 64 ÷ 25

Cross multiplying both the sides we get :

→ 4h² (25) = 64 (r² + h²)

→ 100h² = 64r² + 64h²

→ 100h² - 64h² = 64r²

→ 36h² = 64r²

→ 36 ÷ 64 = r² ÷ h²

Taking square root to the both the sides we get :

→ √(36/64) = r/h

→ 6/8 = r/h

→ 3/4 = r/h

→ 3:4 = r : h

Answer 2

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