Therefore, the volume of the rectangular prism is 84 units cubed.

Click For Summary

Discussion Overview

The discussion revolves around calculating the volume of a rectangular prism given its surface area and two edge measurements. Participants explore the relationship between surface area and volume, applying mathematical reasoning to derive the volume based on provided dimensions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks for help in determining the volume of a rectangular prism with a surface area of 136 square units and edge measurements of 6 and 2.
  • Another participant responds by emphasizing the importance of guiding the original poster rather than providing direct answers, prompting them to share their progress on the problem.
  • A participant claims to have calculated the volume as 84 cubic units, providing a detailed mathematical derivation based on the surface area formula for a rectangular prism.
  • The same participant outlines the steps taken to solve for the height using the surface area equation and subsequently calculates the volume.

Areas of Agreement / Disagreement

There is no explicit consensus on the correctness of the calculations presented, as the discussion includes both requests for help and claims of solutions without further verification or challenge.

Contextual Notes

The discussion does not address potential assumptions regarding the dimensions or the interpretation of the surface area formula, nor does it clarify any dependencies on the definitions of the terms used.

682357
Messages
2
Reaction score
0
What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
 
Mathematics news on Phys.org
Re: Math homework

682357 said:
What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
We are not here to do your homework. We can, however, guide you through.

So what have you been able to do with this problem so far?

-Dan
 
Re: Math homework

I got the answer 84units3 (or cubed)
 
Re: Math homework

682357 said:
What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?

682357 said:
I got the answer 84units3 (or cubed)

The dimensions are length $\ell$, width $w$ and height $h$. Suppose we know $\ell$ and $w$ to be 6 and 2 respectively. A rectangular prism (cuboid) has 3 pairs of matching faces, and it surface area $A$ is given by:

$$A=2(\ell w+\ell h+wh)$$

Using the given surface area and $\ell$ and $w$, we may state:

$$136=2(6\cdot2+6h+2h)$$

$$68=12+8h$$

$$h=7$$

And so the volume $V$ (in units cubed) is given by:

$$V=\ell wh=6\cdot2\cdot7=84\quad\checkmark$$
 

Similar threads

MHB Dimensions of a rectangular prism
  • · Replies 2 ·
Replies
2
Views
2K
High School What are a, b, and c in volume calculations for prisms and pyramids?
  • · Replies 5 ·
Replies
5
Views
3K
MHB Maximum volume using AM GM inequality
  • · Replies 4 ·
Replies
4
Views
3K
Calculate the area intersected by a sphere and a rectangular prism
  • · Replies 4 ·
Replies
4
Views
1K
MHB How Much Netting Does Rita Need to Cover a Rectangular Area?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Maximizing Volume of Rectangular Prism with 120cm x 80cm Sheet Metal
  • · Replies 18 ·
Replies
18
Views
5K
High School Volume of a Cube: Definition & Explanation
  • · Replies 7 ·
Replies
7
Views
5K
Square based prism general rule
  • · Replies 3 ·
Replies
3
Views
2K
MHB [ASK] Find the volume of Pyramid in a Cube
  • · Replies 6 ·
Replies
6
Views
3K
MHB Cfm4life's questions at Yahoo Answers regarding surface areas of solids
  • · Replies 1 ·
Replies
1
Views
3K