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

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

Radius of the sphere = 16/2 = 8 cm
Volume of the sphere = (4/3) x π x 8 x 8 x 8 cm³
Radius of each lead ball = 2/2 = 1 cm
Volume of each lead ball = Volume of sphere / Volume of lead ball

Correct Option: D

Radius of the sphere = 16/2 = 8 cm
Volume of the sphere = (4/3) x π x 8 x 8 x 8 cm³
Radius of each lead ball = 2/2 = 1 cm
Volume of each lead ball = Volume of sphere / Volume of lead ball
= (4/3) π x 1 x 1 x 1 = 4π/3 cm³
∴ Number of lead balls = [(4/3) x π x 8 x 8 x 8 x 3] / [4 π]
= 8 x 8 x 8 = 512

Given that, the diameter of moon is approximately one-fourth of the diameter of Earth.
Let radius on moon = r
Then, radius of Earth = 4r
∴ Volume of Moon/Volume of Earth
= [(4/3)πr³] / [(4/3)π(4r)³]

Correct Option: B

Given that, the diameter of moon is approximately one-fourth of the diameter of Earth.
Let radius on moon = r
Then, radius of Earth = 4r
∴ Volume of Moon/Volume of Earth
= [(4/3)πr³] / [(4/3)π(4r)³]
= [r³] / [64r³] = 1/64 = 1 : 64

According to the question,
Surface area of sphere = Surface area of hemisphere
4πr₁² =3πr₂²
⇒ r₁/r₂ = √3/2

Correct Option: D

According to the question,
Surface area of sphere = Surface area of hemisphere
4πr₁² =3πr₂²
⇒ r₁/r₂ = √3/2
∴ Ratio in volume = [(4/3)πr₁³] / [(4/3)πr₂³]
= 3√3/8 : 1