The surface area of a rectangular prism is 190 square inches, the length is 10 inches, and the width 3 inches. Find the height.
The following areas are equal:
1. Front and Back.
2. Left and right.
3. Top and Bottom.
Therefore, we calculate 3 areas and
multiply each by 2 to get the 6 areas:
As=2(3*h) + 2(10*h) + 2(10*3)=1901n^2.
6h + 20h + 60 = 190,
26h = 190 - 60 = 130,
h = 5in.
To find the height of the rectangular prism, we can use the formula for the surface area:
Surface Area = 2(length × width + length × height + width × height)
Given that the surface area is 190 square inches, the length is 10 inches, and the width is 3 inches, we can substitute these values into the formula:
190 = 2(10 × 3 + 10 × height + 3 × height)
Simplifying this equation, we have:
190 = 2(30 + 10h + 3h)
190 = 2(33 + 13h)
Dividing both sides of the equation by 2:
95 = 33 + 13h
Subtracting 33 from both sides:
62 = 13h
Finally, dividing both sides by 13:
h = 62 / 13
Therefore, the height of the rectangular prism is approximately 4.77 inches.
To find the height of the rectangular prism, we can use the formula for the surface area of a rectangular prism:
Surface Area = 2(length × width) + 2(length × height) + 2(width × height)
Given that the surface area is 190 square inches, the length is 10 inches, and the width is 3 inches, we can substitute these values into the formula:
190 = 2(10 × 3) + 2(10 × height) + 2(3 × height)
Simplifying this equation, we get:
190 = 60 + 20height + 6height
Combining like terms, we have:
190 - 60 = 26height
130 = 26height
Now, to solve for the height, divide both sides of the equation by 26:
height = 130/26 = 5
Therefore, the height of the rectangular prism is 5 inches.
Substitute 4d for e in second equation and solve for d. Insert that value into the first equation and solve for e. Check by inserting both values into the second equation.
See your later post.