1.The surface area of a rectangular prism is 150 cm². If all the sides are tripled, what will the new surface area be?
As=3^2 * 150cm^2 = 9 * 150 = 1350cm^2.
To find the new surface area of a rectangular prism when all sides are tripled, you need to know the formula for surface area of a rectangular prism.
The formula for calculating the surface area of a rectangular prism is given by:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the rectangular prism, respectively.
In this case, we start with a rectangular prism with a surface area of 150 cm². Let's assume the length, width, and height of the initial rectangular prism are l1, w1, and h1, respectively.
Therefore, we have the equation:
2(l1w1 + l1h1 + w1h1) = 150
Now, we triple all sides of the rectangular prism. So the new dimensions will be 3l1, 3w1, and 3h1.
Plugging these new dimensions into the surface area formula, we can calculate the new surface area:
2((3l1)(3w1) + (3l1)(3h1) + (3w1)(3h1))
Simplifying the equation, we get:
2(9l1w1 + 9l1h1 + 9w1h1)
= 18(l1w1 + l1h1 + w1h1)
Hence, the new surface area of the rectangular prism with the tripled sides would be 18 times the initial surface area.
Therefore, the new surface area is:
18 * 150 cm² = 2700 cm².