Could someone pls explain this?

which syllabus is that

I'm afraid we're not psychic.

It's square-based so think of a cuboid. They've said the volume is 18000. And the formula to calculate the volume of a cuboid is width x height x length which is $x * x * h$ and they've just set that to 18000 and rearranged. Hopefully, that clarifies the first bit.

Yeah that makes sense, thank you! Any idea about how they found the surface area?

Like I said, it's a cuboid so it has 2 square sides and 4 rectangular sides. However, it has an open top AND open front so the sum of the areas of the square sides is equal to $x^2$ and the sum of the areas of the rectangular sides is equal to $3xh$.

From the first equation, they've rearranged the volume to find $h$ and then just plugged that into $3xh$. Does that clarify the first 2 parts?

Oh ohh thanks so much! I was finding it very difficult to visualise but looking from your explanation to the solution helped a lot

No problem. I'm guessing the differentiation is straightforward enough

Yeppp just the mensuration part was confusing

The volume and surface area of cuboids and cuboid-like shapes (e.g. here there's an open top and open front) is GCSE work, so you should go back and review it if you find it difficult.

Yeah I did review those mensuration formulas afterwards. Wish these kinds of qs didn't have open ends :/

You're out of luck! Are you on new spec? These questions are designed to be harder and more problem-solving based so you're more likely to have an open-top question,

No I'm actually doing edexcel ial but there have been a lot of qs like that in recent years so I was trying to have a better understanding through online notes and stuff. I always lose most of my marks on optimisation qs and finding the area of shaded regions under graphs

Oh okay. I'm guessing it's mainly the mensuration that messes with people a bit because if you get that bit wrong, the entire question is wrong! Best of luck with any exams you have in the coming months.

No the first part - usually 3 or 5 marks - deals with mensuration where they give a 'Show that' question so even if you don't know how to solve you could just move on the next part using the show that value. The area under graph kind of qs can have 5, 8, 10 or more marks and they're more tricky. Thank you sm!

Ugh.. those q's sound horrible either way.