Theory question 112
Progressions(a) The first term of an Arithmetic progression (A.P) is −8. The ratio of the 7th term to the 9th term is 5:8. Calculate the common difference of the progression.
(b) A sphere of radius 2cm is of mass 11.2g. Find: (i) the volume of the sphere, (ii) the density of the sphere, (iii) the mass of a sphere of the same material but with radius 3cm, [Take π = 22/7]
Show the model answer
Model answer
(a) (−8 + 6d)/(−8 + 8d) = 5/8, so 8(−8 + 6d) = 5(−8 + 8d): −64 + 48d = −40 + 40d, 8d = 24, d = 3.
(b)(i) V = 4/3 × 22/7 × 23 = 704/21 ≈ 33.5 cm3.
(ii) Density = 11.2 ÷ 33.52 ≈ 0.334 g/cm3.
(iii) Mass = density × volume = 0.334 × (4/3 × 22/7 × 27) ≈ 37.8 g (or 11.2 × 27/8 = 37.8 g).
Explanation
Same material means same density; the mass scales with the cube of the radius.