The volume of two spheres are in the ratio 64:27 find their radii if the sum of their radii is 21 cm

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The volumes of two spheres have a ratio of 27:64. Find the area of the larger sphere if the area of the smaller is 18.

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm x 20 cm x 5 cm and the smaller of dimensions 15 cm x 12 cm x 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is र 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.

For bigger boxl = 25 cm b = 20 cm h = 5 cmTotal surface area of the bigger box= 2 (lb + bh + hl)= 2[(25)(20) + (20)(5) + (5)(25)]

= 2[500 + 100 + 125] = 1450 cm2
Cardboard required for all the overlap

∴ Net surface area of the bigger box

= 1450 cm2 + 72.5 cm2 = 1522.5 cm2
∴ Net surface area of 250 bigger boxes
= 1522.5 x 250 = 380625 cm2
Cost of cardboard

For smaller box

l = 15 cm b = 12 cm h = 5 cm∴ Total surface area of the smaller box = 2 (lb + bh + hl)

= 2[(15)(12) + (12)(5) + (5)( 15)] = 2[ 180 + 60 + 75] = 630 cm2
Cardboard required for all the overlaps

= 630 cm2 + 31.5 cm2 = 661.5 cm2 Net surface area of 250 smaller boxes = 661.5 x250 = 165375 cm2
∴ Cost of cardboard

= र 1522.50 + र 661.50 = र 2184.