| Base of a prism of height 10 cm is square. Total surface area of the prism is \[192\,c{{m}^{2}}.\] The volume of the prism is |
A) \[640\,c{{m}^{3}}\]
B) \[160\,c{{m}^{3}}\]
C) \[90\,c{{m}^{3}}\]
D) \[120\,c{{m}^{3}}\]
Correct Answer: B
Solution :
| Height of prism = 10 cm |
| Let the side of square be a cm, |
| Total surface area of prism \[=192\,c{{m}^{2}}\] |
| Now, Perimeter of base \[\times \] Height + 2 \[\times \] Area of base = 192 |
| \[\Rightarrow \] \[4a\times 10+2\times {{a}^{2}}=192\] |
| \[\Rightarrow \] \[40a+2{{a}^{2}}=192\] |
| \[\Rightarrow \] \[2{{a}^{2}}+40a-192=0\] |
| \[\Rightarrow \] \[{{a}^{2}}+20a-96=0\] |
| \[\Rightarrow \] \[{{a}^{2}}+24a-4a-96=0\] |
| \[\Rightarrow \] \[a\,(a+24)-4\,(a+24)=0\] |
| \[\Rightarrow \] \[(a-4)(a+24)=0\] |
| \[\therefore \] \[a=4c{{m}^{2}}\] |
| \[\therefore \] Volume of prism = Area of base \[\times \] Height |
| \[=4\times 4\times 10=160\,c{{m}^{3}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
