Question

solve question number 30 , 31 & 32

Answer 1

Solution. 30)

According to question
V1 + V2 + V3 = V
=> (4/3 pi r1^3) + (4/3 pi r2^3) + (4/3 pi r3^3) = 4/3 pi R^3
=> 4/3 pi ( r1^3 + r2^3 +r3^3) = 4/3 pi R^3
=> r1^3 + r2^3 +r3^3 = R^3
=> 6^3 + 8^3 + 10^3 = R^3
=> 216 + 512 + 1000 = R^3
=> 1728 = R^3
=> R = 12 cm

Radius of new sphere = 12 cm


Solution. 31)

Volume of cuboid = 880 cm^3
L*B*H = 880 ------(1)
Area of Base = 88 cm^2
L*B = 88 ---------(2)

On dividing equation 1 by equation 2, we get

H = 10 cm



Solution. 32)

a^9 + b^9 + 3a^6 b^3 +3b^6 a^3
=> (a^3) ^3 +(b^3) ^3 + 3a^3 b^3 (a^3 +b^3)
=> (a^3 +b^3) ^3