MAT Exam 2022 Paper

Concept:Use the volume formula to find the height, then use the slant height to find the total surface area.Explanation:Base is a square with side $10$ cm.Base area $= 10 \times 10 = 100 \, \text{cm}^2$.Volume of pyramid is $V = \frac{1}{3} \times \text{Base Area} \times \text{height}$.Given $V = 400$, so $400 = \frac{1}{3} \times 100 \times h$.Therefore, height $h = 12$ cm.Slant height is the hypotenuse of a right triangle with height $12$ cm and half-side $5$ cm.So slant height $l = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = 13$ cm.Lateral surface area $= \frac{1}{2} \times \text{perimeter} \times \text{slant height}$.Perimeter of base $= 4 \times 10 = 40$ cm.Lateral surface area $= \frac{1}{2} \times 40 \times 13 = 260 \, \text{cm}^2$.Total surface area $= \text{Lateral surface area} + \text{Base area}$.Total surface area $= 260 + 100 = 360 \, \text{cm}^2$.Answer:Option C: $360 \, \text{cm}^2$.