The surface area of the new figure is 1470 square meters, if the edge length of the smaller cube is half the edge length of the cube below and edge length of bottom cube is 14 m.
Step-by-step explanation:
The given is,
Length of Bottom (larger) cube is 14 meters
Step:1
Surface area of new figure = (Surface area of smaller cube) +
(Surface area of bottom (larger) cube)....(1)
Step:2
Surface area of Bottom(larger) cube is,
[tex]Surface area, A = 6a^{2}[/tex]..............................................(2)
From given, a = 14 m
Equation (2) becomes,
[tex]=6(14)^{2}[/tex]
[tex]=(6)(196)[/tex]
[tex]=1176[/tex]
Surface area of bottom cube, A = 1176 square meters
Step:3
Surface area of smaller (top) cube is,
[tex]Surface area, A = 6a^{2}[/tex]....................................................(3)
From given, a = 7 m ( ∵ The edge length of the smaller cube is half the edge length of the cube below)
Equation (2) becomes,
[tex]=6(7)^{2}[/tex]
[tex]=(6)(49)[/tex]
[tex]=294[/tex]
Surface area of bottom cube, A = 294 square meters
Step:4
From equation (1),
Surface area of new figure = 1176 + 294
= 1470
Surface area of new figure = 1470 square meters
Result:
The surface area of the new figure is 1470 square meters, if the edge length of the smaller cube is half the edge length of the cube below and edge length of bottom cube is 14 m.
The surface area of the new figure is 1421 square meters
The surface area of a cube is:
[tex]A = 6l^2[/tex]
The side length of the big cube is 14 m.
So, the surface area is:
[tex]A_1 = 6 * 14^2[/tex]
[tex]A_1 = 1176[/tex]
The side length of the small cube is 7 m.
So, the surface area of the visible sides of the small cube is:
[tex]A_2 = (6 -1) * 7^2[/tex]
[tex]A_2 = 245[/tex]
The surface area of the shape is then calculated as:
[tex]A = A_1 + A_2[/tex]
This gives
[tex]A = 1176 + 245[/tex]
[tex]A = 1421[/tex]
Hence, the surface area of the new figure is 1421 square meters
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