Lateral surface area of a cube is 420 cm2 less than the lateral surface area of a cylinder. Height of cylinder is 2R cm and radius is R cm. If the side of cube is equal to the radius of the cylinder, find the approximate area of circle whose radius is (R + 3) cm. ?

Question

Lateral surface area of a cube is 420 cm2 less than the lateral surface area of a cylinder. Height of cylinder is 2R cm and radius is R cm. If the side of cube is equal to the radius of the cylinder, find the approximate area of circle whose radius is (R + 3) cm. ?

314 cm²
290 cm²
340 cm²
388 cm²
225 cm²

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 314 cm2

Given:

Lateral surface area of a cube = 420 cm² less than the lateral surface area of a cylinder.

Height of cylinder = 2R cm

Radius = R cm

The radius of circle = (R + 3) cm

Formula used:

Lateral surface area of cube = 4a²

Lateral surface area of cylinder = 2πrh

Area of circle = πr²

Calculation:

According to the question

⇒ 4R² = 2πR × 2R – 420

⇒ 4R² = 22/7 × 4R² – 420

⇒ 4R²(22/7 – 1) = 420

⇒ 4R²(22 – 7)/7 = 420

⇒ 4R²(15/7) = 420

⇒ 60R²/7 = 420

⇒ R²/7 = 7

⇒ R² = 49

⇒ R = 7 cm

Now,

The radius of circle = (R + 3) = (7 + 3) = 10 cm

Area of circle = πR²

⇒ 22/7 × 10 × 10 cm²

⇒ 2200/7 cm²

⇒ 314.28 cm² ~ 314 cm²

∴ The required value of circle is 314 cm².