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The base of a right prism, whose height ...

The base of a right prism, whose height is 2 cm, is a square. If the total surface area of the prism is `10 cm^(2)`, then its volume is :

A

`2 cm^2`

B

`1 cm^3`

C

`4 cm^3`

D

`3 cm^3`

Text Solution

Verified by Experts

The correct Answer is:
A
Total surface area of prism = perimeter of Base `xx` Height +2 `xx` Base Area
`10 =4a xx 2 +2 xx a^2`
` 10 = 8a + 2a ^2`
` a^2 =8a +2a^2`
a^2 +4a -5=0`
`( a +5 ) (a-1)=0`
` a=1 ,a=-5`
Volume of Prism = Ara of base `xx` height
` 1 xx 1 xx 2 = 2 cm^3`
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