Q1 A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Answers & Comments
Answer:
Let’s solve this problem step by step.
Part (i): The lateral surface area of a cubical box is given by the formula 4a^2, where a is the length of each edge of the cube . Substituting a=10 cm, we get the lateral surface area of the cubical box as 4*10^2 = 400 cm^.
The lateral surface area of a cuboidal box is given by the formula 2h(l+b), where h, l, and b are the height, length, and breadth of the cuboid, respectively 1. Substituting h=8 cm, l=12.5 cm, and b=10 cm, we get the lateral surface area of the cuboidal box as 2*8*(12.5+10) = 440 cm^.
Therefore, the cuboidal box has a greater lateral surface area than the cubical box by (440-400) = 40 cm^.
Part (ii): The total surface area of a cubical box is given by the formula 6a^2, where a is the length of each edge of the cube . Substituting a=10 cm, we get the total surface area of the cubical box as 6*10^2 = 600 cm^.
The total surface area of a cuboidal box is given by the formula 2(lb+bh+hl), where h, l, and b are the height, length, and breadth of the cuboid, respectively . Substituting h=8 cm, l=12.5 cm, and b=10 cm, we get the total surface area of the cuboidal box as 2*(12.5*10 + 10*8 + 8*12.5) = 610 cm^.
Therefore, the cubical box has a smaller total surface area than the cuboidal box by (610-600) = 10 cm^2.