Respuesta :
Answer:
The surface area of the enlarged prism is, 376 cm²
Step-by-step explanation:
Surface area of the prism(S) is given by:
[tex]S =2(lw+wh+hl)[/tex]
where, l is the length , w is the width and h is the height of the prism receptively.
Given that:
A right rectangular prism has a length of 5 cm, a width of 4 cm, and a height of 3 cm.
⇒ l = 5 cm , w = 4 cm and h = 3 cm
Since, the dimensions of the prism are doubled
⇒[tex]l=2 \cdot 5 = 10 cm[/tex]
[tex]w =2 \cdot 4 = 8 cm[/tex] and
[tex]h =2 \cdot 3 = 6 cm[/tex]
Substitute these in [1] we have;
[tex]S = 2(10 \cdot 8 + 8 \cdot 6 + 6 \cdot 10) = 2(80+48+60) = 2(188) = 376 cm^2[/tex]
Therefore, the surface area of the enlarged prism is, 376 cm²
If the dimensions of the prism are doubled the surface area of the enlarged prism is 376 cm²
Surface area of a rectangular prism:
- Area = 2lw + 2lh + 2wh
where
h = height
l = length
w = width
Therefore, if the dimension of the prism are doubled the new dimension will be as follows:
l = 5(2) = 10 cm
w = 4(2) = 8 cm
h = 3(2) = 6 cm
Therefore,
surface area = 2(10 × 8) + 2(10 × 6) + 2(6 × 8)
surface area = 2(80) + 2(60) + 2(48)
surface area = 160 + 120 + 96
surface area = 376 cm²
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