Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3πr³ = πr²h

Correct Option: D

Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3πr³ = πr²h
⇒ h = 4r/3
⇒ 4r = 3h
⇒ 2r = 3/2h
⇒ 2r/h = 3/2
∴ Required ration = 3 : 2

Volume of 1 bullet = 4/3π(2)³ = (32/3 x 22/7) cm³
Volume of the cube = (44)³

Correct Option: B

Volume of 1 bullet = 4/3π(2)³ = (32/3 x 22/7) cm³
Volume of the cube = (44)³
∴ Number of bullets = Volume of solid/Volume of 1 bullet
= (44)³ x 3 x 7 / 32 x 22 = 2541

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

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