So I am back on the Surface! [Part I]

Geometry Level 1

My dad, Asgore has recently sliced a pineapple in a cool way using his trident! I say this because it is very smooth on the outside and the inside, just like a perfect cylinder. He removed the core as well, and separated both of them as perfect cylinders, like the picture below, but smoother, cuz' his trident is magic :)

Which brings upon a question, what is the volume of the clean pineapple now? Answer to two decimal places...

The internal cylinder has a height of 5 5 and a radius of 3 3

The large cylinder as a whole has a height of 5 5 (obviously...) and a radius of 13 13


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The answer is 2513.28.

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3 solutions

Volume = Total volume Small cylinder volume = π R 2 h π r 2 h = π h ( R 2 r 2 ) = π × 5 × ( 169 9 ) 2513.27 \begin{aligned} \text{Volume} &=\text{Total volume}-\text{Small cylinder volume} \\ &=\pi R^2 h -\pi r^2 h \\ &=\pi h (R^2-r^2) \\ &=\pi \times 5 \times (169-9) \\ &\approx \boxed{2513.27} \end{aligned}

@Vinayak Srivastava - We posted similar solution, but you didn't align your equations, would you like to learn how???

A Former Brilliant Member - 10 months, 2 weeks ago

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I know how to align, but I wrote a single line.

Vinayak Srivastava - 10 months, 2 weeks ago

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Why don't you like aligning? Aligning my equation makes me feel satisfied :)

A Former Brilliant Member - 10 months, 2 weeks ago

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@A Former Brilliant Member I don't say I don't like it, but it is not needed for this problem.

Vinayak Srivastava - 10 months, 2 weeks ago

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@Vinayak Srivastava Ok, your choice, nice solution btw, upvoted!

A Former Brilliant Member - 10 months, 2 weeks ago

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@A Former Brilliant Member Thank you! If you want, let me align it.

Vinayak Srivastava - 10 months, 2 weeks ago

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@Vinayak Srivastava Your choice, i like solution for its content, not looks :)

A Former Brilliant Member - 10 months, 2 weeks ago

Cool! Great job!

A Former Brilliant Member - 10 months, 2 weeks ago

@Vinayak Srivastava , how did you find my problem? You seem to have found it first and solved it first...

Anyway, nice solution! Upvoted!

Frisk Dreemurr - 10 months, 2 weeks ago

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Thank you! I think I found it in New section of Community tab.

Vinayak Srivastava - 10 months, 2 weeks ago

My Dad's trident is cooler than your dad's, Frisk.

Cylinder Volume Formula = π r 2 h \textsf{Cylinder Volume Formula} = \pi r^{2} h (Where r r is radius of the cylinder and h h is the height)

P i n e a p p l e V o l u m e = T o t a l C y l i n d e r V o l u m e H o l l o w S p a c e V o l u m e = 1 3 2 π × 5 3 2 π × 5 = 845 π 45 π = 800 × π = 2513.274 2513.27 \begin{aligned} Pineapple \ Volume \ &= \ Total \ Cylinder \ Volume \ - \ Hollow \ Space \ Volume \\ &= 13^{2} \pi \times 5 - 3^{2} \pi \times 5 \\ &= 845 \pi - 45 \pi \\ &= 800 \times \pi \\ &= 2513.274 \ldots \\ &\approx \boxed{2513.27} \end{aligned}

Frisk Dreemurr
Jul 28, 2020

@Percy Jackson

I made a question related to my father, he is so cool!

My Dad's cooler than a monster :)

A Former Brilliant Member - 10 months, 2 weeks ago

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