Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
A closed box with a square or rectangular base will be a cuboid. To find the volume of this box let's know the things given in the question,
- Closed box with a square base with each side of 'x' units.
- Height of the box = y units
- Surface area of the box = 12π square feet
Volume of a cuboid will be given by,
V = Length × Width × Height
Substitute the measures in the expression,
V = [tex]x\times x\times y[/tex] [Since, base is a square]
V = [tex]x^2y[/tex] ---------(1)
Since, surface area of a cuboid is given by,
S = 2(lb + bh + hl)
Here, l = Length, b = width and h = height
Therefore, S = [tex]2(x\times x)+2(x\times y)+2(y\times x)[/tex]
S = [tex]2(x^2+2xy)[/tex]
Now substitute the value of Surface area,
12π = [tex]2(x^2+2xy)[/tex]
[tex]y=\frac{6\pi-x^2}{2x}[/tex]
By substituting the value of y in expression (1),
[tex]V=\frac{x^2(6\pi-x^2)}{2x}[/tex]
Therefore, expression for the volume of the box will be [tex]V=\frac{x^2(12\pi-x^2)}{2x}[/tex]
Learn more,
https://brainly.com/question/10541659
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
