erma0902
Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Aina builds a cube model out of manila cards. If the volume of the constructed cube is (2+3p) ³ cm³, find the total surface area of the cube in terms of p.

HELPPPP

Sagot :

Given:

The volume of a cube = [tex](2+3p)^3\ \text{cm}^3[/tex]

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

[tex]V=a^3[/tex]            ...(i)

Where, a is the side length.

It is given that,

[tex]V=(2+3p)^3\ \text{cm}^3[/tex]         ...(ii)

On comparing (i) and (ii), we get

[tex]a=2+3p\text{ cm}[/tex]

Now, the total surface area of a cube is:

[tex]A=6a^2[/tex]

Where, a is the side length.

Putting [tex]a=2+3p[/tex], we get

[tex]A=6(2+3p)^2[/tex]

Therefore, the total surface area of the cube in terms of p is [tex]6(2+3p)^2\ \text{cm}^2[/tex].

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.