# Thread: volume bounded by different region

1. ## volume bounded by different region

Well , i have 2 questions here :
part a :
I'm asked to find the volume bounded by plane y +z = 1 , y = (x^2) , xy plane and yz plane

part b :

I'm asked to find the volume bounded by plane y +z = 1 , y = (x^2) ,and z = 0 ...

the ans given for part a is 4/15 , for part b is 8/15

However , i cant imagine the solid bounded by the region in part b ....

For part a , i suspect the ans is wrong ...

2. ## Re: volume bounded by different region

for part (a)

$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 1$

for part (b)

x from -1 to 1

3. ## Re: volume bounded by different region

Originally Posted by Idea
for part (a)

$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 1$

for part (b)

x from -1 to 1
Is there anything wrong with the diagram ?

4. ## Re: volume bounded by different region

Originally Posted by Idea
for part (a)

$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 1$

for part (b)

x from -1 to 1
do you mean for part b , the diagram look like this ? We have to draw the plane y +z = 1, first , then form the tip , join them to x = 1 and x = -1 ?

5. ## Re: volume bounded by different region

Originally Posted by xl5899
do you mean for part b , the diagram look like this ? We have to draw the plane y +z = 1, first , then form the tip , join them to x = 1 and x = -1 ?

If so, I only get 7/15, not 8/15

6. ## Re: volume bounded by different region

the diagram looks OK. answer should be 8/15

7. ## Re: volume bounded by different region

Originally Posted by Idea
the diagram looks OK. answer should be 8/15
Can you show ur working? I tried to calculate manually and using Calc, but get 7/15....

8. ## Re: volume bounded by different region

$\displaystyle y$ from $\displaystyle x^2$ to $\displaystyle 1$