17 Views

Question : The base of the right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm2, then its volume is:

Option 1: 3 cm3

Option 2: 1 cm3

Option 3: 2 cm3

Option 4: 4 cm3


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 12th Jan, 2024

Correct Answer: 2 cm3


Solution : Height = 2 cm
The total surface area of the prism = 10 cm2
Let the side of the base be $a$ cm.
The total surface area of the prism = curved surface area + 2 × area of base
10 = perimeter of base × height + 2 × area of base
⇒ (4 × $a$ × 2) + (2 × $a^2$) = 10
⇒ $a^2 + 4a -5$ = 0
⇒ $(a+5)(a-1)$ = 0
Since $a$ cannot be negative,
$a$ = 1
Volume = base area × height
= $(1)^2 × 2$
= 2 cm3
Hence, the correct answer is 2 cm3.

Know More About

Related Questions

Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books