Solution: 

Volume of sphere = 4/3 π r³
= (4/3) X (22/7) X (4.2)³ = 310.464 cubic cm

Mass = volume X density
= 310.464 X 8.9
= 2763.1296 gm = 2.76 kg

Solution: 

Volume of two similar shapes are in triplicate ratio of their dimensions. For example; if radii are R and r then ratio of volumes = R³ : r³
Hence, volume of earth/volume of moon
= 4³ : 1³
= 64 : 1

Solution: 

Volume of hemisphere = 2/3 π r³
= (2/3) X (22/7) X (5.25)³ = 303.1875 cubic cm = 0.303 litre

Solution: 

Inner radius r = 1 m, outer radius r = 1.01 m
Volume of metal = 4/3 π (R³ - r³)
= (4/3) X (22/7) [(1.01)³ - 1³]
= (4/3) X (22/7) X 0.030301 = 0.06348 cubic m

Solution: 

Surface area of sphere = 4 π r²
Or, 154 = 4 X (22/7) X r²
Or, r² = (154 X 7)/(22 X 4) = 49/4
Or, r = 7/2 = 3.5 cm

Volume of sphere = 4/3 π r³
= (4/3) X (22/7) X (3.5)³ = 179.67 cubic cm

Solution: 

Curved surface area of hemisphere = cost/rate
= 498.96/2 = 249.48 sq m
Or, 2 π r² = 249.48
Or, r² = (249.48 X 7)/(2 X 22)
Or, r = 6.3 m

Volume of hemisphere = 2/3 π r³
= (2/3) X (22/7) X (6.3)³ = 523.908 cubic m

Solution: 

Here; ratio of volumes = 27 : 1
Radii shall be in sub-triplicate ratio, i.e. 3 : 1
Because 3³ : 1³ = 27 : 1
Now, surface areas shall be in duplicate ratio of radii
Hence, ratio of surface areas = 3² : 1² = 9 : 1

Solution: 

Volume of sphere = 4/3 π r³
= (4/3) X (22/7) X (1.75)³
= 22.46 cubic mm