Question

Tunisha wants to build a cubical shaped pet house for her dog. She had a wild thought of decreasing the length by 5%, decreasing the breadth by 5% and increasing the height by 20%. She now wants to know the percentage change in the surface area of the pet house. Can you help?
Note: Find the approx figure
Options

7.25%

5.62%

8.33%

6.1%

Answer 1

Percentage increase in the surface area will be approximately equal to 6.1%.

• Tunisha wants to build a pet house for her dog in the shape of the cube.

• Let the length, breadth and height of the cube be 20 , 20, 20 units.

• Total surface area of the cuboid will be 2(lb+bh+hl)= 2(400+400+400) =2400 sq units.

• Now the length is decreased by 5% , breadth is decreased by 5% and height is increased by 20%.

• Now the length becomes 19 , breadth becomes 19 and height becomes 24 units.

• New Total surface area of the cuboid will be 2(361+456+456) = 2546 sq. units

• Now the increase in the surface area will be :

• Percentage increase will be = $\frac{New TSA - TSA}{TSA}$ × 100

Percentage increase will be = $\frac{2546 - 2400}{2400}$ × 100

Percentage increase will be = $\frac{146}{2400}$ × 100 = 0.060833 × 100

• Percentage increase will be ≈ 6.1 %