Mathematics
Three cubes of silver with edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube. Find the cost of coating the surface of the new cube with gold at the rate of ₹3.50 per square centimeter.
Answer
By formula,
Volume of cube = (edge)3
Volume of first cube = (3)3
= 3 × 3 × 3
= 27 cm3.
Volume of second cube = (4)3
= 4 × 4 × 4
= 64 cm3
Volume of third cube = (5)3
= 5 × 5 × 5
= 125 cm3.
Total volume = 27 + 64 + 125 = 216 cm3.
So, new cube's volume = 216 cm3
Let length of edge of new cube = x cm.
⇒ (x)3 = 216
⇒ (x)3 = (6)3
⇒ x = 6 cm.
Surface area of new cube = 6(x)2
= 6.(6)2
= 6 × 6 × 6
= 216 cm2.
Given,
Cost of coating the surface for 1 cm2 = ₹3.50
So, the cost of coating the surface for 216 cm2 = ₹3.50 × 216 = ₹756.
Hence, cost of coating the surface of new cube = ₹756.
Related Questions
The external dimensions of an open rectangular wooden box are 98 cm by 84 cm by 77 cm. If the wood is 2 cm thick all around, find
(i) the capacity of the box
(ii) the volume of the wood used in making the box, and
(iii) the weight of the box in kilograms correct to one decimal place, given that 1 cm3 of wood weighs 0.8 g.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0.25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹1.25 per square centimeter?
The adjoining figure shows a victory stand, each face is rectangular. All measurements are in centimetres. Find its volume and surface area (the bottom of the stand is open).
