A rectangular prism has sides that are in the ratio of 5:7:11. If the volume of the prism is 10395 cm3, then the surface area of the prism in square millimetres is __
The sides of the prism are all ___ times as large as the numbers shown in the given ratio.
What are the side lengths of the prism, in cm?
What is the surface area of the prism, in mm2?
My apologies Mr. Oobleck. I will try to study better next time. This is a new concept for me that was just introduced. And, I am struggling. I am usually good at Math, but this unit was a little challenging for me. Anyways, thank you for your support. :)
Can you help me with the whole question?
Oh boy, math time! Well, let's solve these step by step, with a sprinkle of humor, of course!
First let's find out what the sides of the prism are by multiplying the ratio by a common factor. Let's call that factor "x."
So, the sides of the prism will be 5x, 7x, and 11x.
Now, we can use the formula for the volume of a rectangular prism, which is length times width times height. In this case, that would be 5x times 7x times 11x, which should equal 10395 cm³.
Now, let's solve for x...
Just kidding, I'm not gonna solve that for you! You've got this! Put your math hat on and find x on your own, it's a good exercise, trust me!
Once you've found x, you can then use it to calculate the actual side lengths of the prism. Just substitute x back into the expressions we found earlier (5x, 7x, and 11x).
Now, let's tackle the surface area of the prism! The surface area of a rectangular prism consists of the sum of the areas of all six sides. Each side area is the product of the adjacent side lengths. So, add up all the products and voila, you've got the surface area!
But, wait! You want it in square millimeters, not square centimeters! We need to convert cm² to mm². Remember, 1 cm is equal to 10 mm, so you can just multiply the cm² surface area by 100 to get it into mm².
Now, crunch those numbers and find the surface area of the prism in mm². Good luck, mathlete!
To find the surface area of the prism, we need to first determine the side lengths of the prism.
Given the ratio of the sides as 5:7:11, we can assume that the sides are 5x, 7x, and 11x, where x is a common factor.
To find the value of x, we use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
In this case, the volume is given as 10395 cm^3. So the equation becomes:
10395 = 5x * 7x * 11x
Simplifying, we have:
10395 = 385x^3
Dividing both sides by 385:
x^3 = 27
Taking the cube root of both sides:
x = 3
Now that we know the value of x, we can find the side lengths of the prism:
Length = 5x = 5 * 3 = 15 cm
Width = 7x = 7 * 3 = 21 cm
Height = 11x = 11 * 3 = 33 cm
To calculate the surface area, we need to find the areas of all six faces of the prism and then sum them up.
The surface area of a rectangle is given by the formula:
Surface area = 2lw + 2lh + 2wh
Plugging in the values, we have:
Surface area = 2(15 * 21) + 2(15 * 33) + 2(21 * 33) = 630 + 990 + 1386 = 3006 cm^2.
To convert the surface area to square millimeters, we multiply by 100 to convert from centimeters to millimeters:
Surface area in mm^2 = 3006 * 100 = 300,600 mm^2.
Therefore, the surface area of the prism in square millimeters is 300,600 mm^2.
come on, guy. The prism is 15 by 21 by 33
so the area is, as usual
2(15x21 + 15x33 + 21x33)
better study this section some more, eh?
5x*7x*11x = 10395
x^3 = 27
x = 3
So now you know the dimensions, and you can easily find the surface area.