Question

a rectangular metal block X measuring 12cm by 8cm by 4cm, is melted and recast into a rectangular block Y, 2cm wide and 1cm high. find the length of metal block Y. find the ratio of the total surface area of block X to that of block Y.​

Answer 1

Answer:

Step-by-step explanation:

Let Length,breadth, Height and Volume be L₁, L₂, B₁, B₂, H₁, H₂, V₁, V₂ accordingly to each cases

Given L₁, B₁, H₁= 12, 8, 4

so, V₁= 12×8×4

=32×12

=384 cm³

In the given question, V₁= V₂

L₂, B₂, H₂= 2, 1, H₂

V₂=2×1×H₂

⇒384=2×H₂

⇒H₂=384/2=192 cm

Let the TSA's be S₁ and S₂ accordingly

S₁=2(12×8+8×4+12×4)

=2(96+32+48)

2(176)=352 cm²

S₂=2(2×1+1×192+2×192)

=(2+192+384)

=578 cm²

⇒S:S = 352:578= 176:289