A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (a) Which box has the greater lateral surface area and by how much? (b) Which box has the smaller total surface area and by how much? (c) Which box has the greater volume and by how much?
Answers
Step-by-step explanation:
Given:-
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm hight.
To find:-
(a) Which box has the greater lateral surface area and by how much?
(b) Which box has the smaller total surface area and by how much?
(c) Which box has the greater volume and by how much?
Solution:-
Edge of a cubical box = 10 cm
we know that
The lateral surface area of a cube of the side 'a' units is 4a^2 sq.units
We have a = 10 cm
Lateral surface area of the given cubical box
=>4(10)^2 sq.cm
=>4×10×10
=>400 sq.cm
Lateral surface area of the cubical box
=400 sq.cm-----------(1)
We know that
The Total surface area of a cube of the side 'a' units is 6a^2 sq.units
Total surface area of the given cubical box =
=>6(10)^2 sq.cm
=>6×10×10 sq.cm
=>600 sq.cm
Total surface area of the cubical box
= 600 sq.cm-----------(2)
We know that
Volume of a cube of the side a units = a^3 cubic units
Volume of the given cubical box = 10^3 cubic.cm
=>10×10×10 cubic cm
Volume of the cubical box = 1000 cubic cm----(3)
And given that
Length of the cuboidical box (l)=12.5cm
Width of the cuboidical box (b)=10 cm
Height of the cuboidical box (h)=8 cm
We know that
Lateral surface area of a cuboid = 2h(l+b) sq.units
Lateral surface area of the given cuboidical box
=>2×8(12.5+10) sq.cm
=>16×(22.5) sq.cm
=>360 sq.cm
Lateral surface area of the cuboidical box
= 360 sq.cm----------(4)
We know that
Total surface area of a cuboid = 2(lb+bh+hl) sq.units
=>2[(12.5×10)+(10×8)+(8×12.5)] sq.cm
=>2(125+80+100) sq.cm
=>2(305) sq.cm
=>610 sq.cm
Total surface area of the given cuboidical box =
610 sq.cm----------(5)
We know that
Volume of a cuboid = lbh cubic units
=>12.5×10×8 cubic cm
=>1000 cubic cm
Volume of the given cuboidical box
= 1000 cubic. cm----------(6)
Now ,
From (1) and (4)
400 sq.cm >360 sq.cm
LSA of the cubical box > LSA of the cuboidical box
=>400 sq.cm - 360 sq.cm
= 40 sq.cm
The cubical box is 40 sq.cm more lateral surface area than that of the cuboidical box .
From (2) and (5)
600 sq.cm < 610 sq.cm
TSA of the cubical box < TSA of the cuboidical box
610 sq.cm -600 sq.cm = 10 sq.cm
The cubical box is 10 sq.cm less total surface area than that of the cuboidical box.
From (3) and (6)
1000 cubic cm = 1000 cubic cm
Volume of the cubical box = Volume of the cuboidical box
The volume of the cubical box is equal to the volume of the cuboidical box
Both are having same volumes.
Answer:-
a) Cubical box has more lateral surface area by 40 sq.cm
b)The cubical box has less total surface are by
10 sq.cm
c)Both are having same volumes.
Used formulae:-
Cube:-
- The lateral surface area of a cube of the side 'a' units is 4a^2 sq.units
- The Total surface area of a cube of the side 'a' units is 6a^2 sq.units
- Volume of a cube of the side a units = a^3 cubic units
Cuboid:-
- Lateral surface area of a cuboid = 2h(l+b) sq.units
- Total surface area of a cuboid = 2(lb+bh+hl) sq.units
- Volume of a cuboid = lbh cubic units
Answer:
cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (a) Which box has the greater lateral surface area and by how much? (b) Which box has the smaller total surface area and by how much? (c) Which box has the greater volume and by how much?
Step-by-step explanation:
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