Let the diameter's of two sphere are d₁ and d₂, respectively.
∴ Ratio of their surface areas = 4πr₁²/4πr₂²

Correct Option: A

Let the diameter's of two sphere are d₁ and d₂, respectively.
∴ Ratio of their surface areas = 4πr₁²/4πr₂²
= (2r₁)²/(2r₂)² = d₁²/d₂²
= (d₁/d₂)² = (3/5)² = 9/25 = 9 : 25

Volume of small spheres
= Volume of bigger sphere / Number of small spheres = [(4/3)π(4)³] / 64
= [(4/3) x π x 4 x 4 x 4] / 64
= 4/3 π cm³

Let radius of small sphere be r
∴ 4/3πr³ = 4π/3
⇒ r² = 1 cm

Correct Option: C

Volume of small spheres
= Volume of bigger sphere / Number of small spheres = [(4/3)π(4)³] / 64
= [(4/3) x π x 4 x 4 x 4] / 64
= 4/3 π cm³

Let radius of small sphere be r
∴ 4/3πr³ = 4π/3
⇒ r² = 1 cm
Now, surface area of small sphere = 4πr² = 4π cm²

Curved surface area = 2πr²

Correct Option: A

Curved surface area = 2πr²
= 2π x 14 x 14 = 2 x (22/7) x 14 x 14
= 2 x 22 x 2 x 14
= 88 x 14
= 1232 sq cm

Given,
Diameter = 2 cm
∴ r = 1 cm
Now, Total surface area of hemisphere = 3πr²
and curved surface area = 2πr²
Required difference = 3πr² - 2πr² = πr²

Correct Option: C

Given,
Diameter = 2 cm
∴ r = 1 cm
Now, Total surface area of hemisphere = 3πr²
and curved surface area = 2πr²
Required difference = 3πr² - 2πr² = πr²
= π x 1² = π sq cm

Let radius of the third sphere be r.
Then, 4/3 π x (12)³ = 4/3 π x (6)³ + 4/3π x (8)³ + 4/3 πr³

Correct Option: C

Let radius of the third sphere be r.
Then, 4/3 π x (12)³ = 4/3 π x (6)³ + 4/3π x (8)³ + 4/3 πr³
⇒ (12)³ = (6)³ + (8)³ + r³
⇒ r³ = 1728 - 216 - 512
⇒ r³ = 1000
∴ r = 10 cm