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

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

Curved surface area of the hemisphere = 2πr²
= 2 x (22/7) x (7/2) x (7/2) = 77 sq
As bowl is to painted inside and outside.
∴ Total surface to be painted = 77 x 2 = 154 sq cm
∴ Cost of painting 154 sq cm = (5/10) x 154

Correct Option: D

Curved surface area of the hemisphere = 2πr²
= 2 x (22/7) x (7/2) x (7/2) = 77 sq
As bowl is to painted inside and outside.
∴ Total surface to be painted = 77 x 2 = 154 sq cm
∴ Cost of painting 154 sq cm = (5/10) x 154 = 1/2 x 154 = ₹ 77

Curved surface area of the sphere = 4πr²
Volume of the sphere = (4/3)πr³

Correct Option: A

Curved surface area of the sphere = 4πr²
or 616 = 4πr²
⇒ πr² = 616/4 = 154
⇒ r² = (154 x 7) / 22 = 49
∴ r = √49 = 7 cm
∴ Volume of the sphere = (4/3)πr³
= (4/3) x (22/7) x 7 x 7 x 7
= 4312 / 3 cm³