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Omni-MATH / Harvard has recently built a new house for its students consisting of n levels, where the k th level from the top can be modeled as a 1-meter-tall cylinder with radius k meters. Gi…

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problem

Harvard has recently built a new house for its students consisting of nn levels, where the kk th level from the top can be modeled as a 1-meter-tall cylinder with radius kk meters. Given that the area of all the lateral surfaces (i.e. the surfaces of the external vertical walls) of the building is 35 percent of the total surface area of the building (including the bottom), compute nn.
Plain-text mathematical notation (without MathML)
Harvard has recently built a new house for its students consisting of n levels, where the k th level from the top can be modeled as a 1-meter-tall cylinder with radius k meters. Given that the area of all the lateral surfaces (i.e. the surfaces of the external vertical walls) of the building is 35 percent of the total surface area of the building (including the bottom), compute n.
Original LaTeX notation
Harvard has recently built a new house for its students consisting of $n$ levels, where the $k$ th level from the top can be modeled as a 1-meter-tall cylinder with radius $k$ meters. Given that the area of all the lateral surfaces (i.e. the surfaces of the external vertical walls) of the building is 35 percent of the total surface area of the building (including the bottom), compute $n$.

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Source and history

task_id
12c84e03-d0d3-559f-b890-06a3e50f83d8
task_key
test--12c84e03-d0d3-559f-b890-06a3e50f83d8
task_revision_id
1
config / split
/ test

Official source

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