Question

Find the dimensions of the cuboid.
3. The dimensions of a rectangular box are in the ratio of
2:3:4 and the difference between the cost of covering
it with a sheet of lead at Rs. 8 and Rs. 10 per sq m is
Rs. 234. Find the length, breadth and height of the box.
14. If each edge is increased by 25%. find the percentage
increase in its surface area.
5. The cost of carpeting a room is Rs. 2.50 per sq. m is
Rs. 450. The cost of white-washing the walls at 50
paise per m is Rs. 135. The room is 12 m wide. Find
its height.​

Answer 1

Answer:

3.

Let the dimensions be 2x, 3x and 4x respectively.

Total cost of covering = Rs 234

=Rs 8/10 × TSA of cuboid = Rs 234

=0.8×2(2x× 3x +3x×4x + 4x×2x)=234

= 1.6(6x²+12x²+8x²)=234

= 1.6×26x²=234

=x²=234/1.6×26

=x²=234/41.6

=x²=5.625

=x=√5.625

= x=2.3

Thus, dimensions are

2x=2×2.3=4.6m

3x=3×2.3=6.9m

4x=4×2.3=9.2m

5.

Breadth = 12 m

Cost of carpeting = Rs 450

= Rs 2.50×Area of rectangle=Rs 450

=2.50×(l×b) =450

=2.50× length × 12=450

= length =450/(2.50×12)

= length = 450/30

=15m

Cost of whitewashing walls=Rs 135

=50 paise ×2(l+b)h= 135

=Rs 0.50 × 2(15+12)h = 135

=0.50 × 2 × 27 × h= 135

= 27×h = 135

= h =135/27

= h = 5 m