MATHEMATICS HIGH SCHOOL

Which solid has a volume that is 3 times the volume of a cone with the same base and height?a.cylinder
b.prism
c.pyramid eliminate
d.sphere?

Answers

Answer 1
Answer: Answer: (a) Cylinder

The formula for volume of a cone = 1/3 π r² h

The formula for volume of a cylinder = π r² h
Answer 2
Answer: The answer is  A. Cylinder

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Please help me on this

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y+x=8\n y=8-x\n\n (12)/(x)=8-x\qquad x\not=0\n 12=8x-x^2\n x^2-8x+12=0\n x^2-8x+16-4=0\n (x-4)^2=4\n x-4=2 \vee x-4=-2\n x=6 \vee x=2\n\n y=8-6 \vee y=8-2\n y=2 \vee y=6\n \boxed{(x,y)=\{(2,6),(6,2)\}}

\displaystyle S_P=\int\limits_2^68-x-(12)/(x)\, dx\n S_P=\left[8x-(x^2)/(2)-12\ln x\right]_2^6\n S_P=8\cdot6-(6^2)/(2)-12\ln 6-(8\cdot2-(2^2)/(2)-12\ln 2)\n S_P=48-18-12\ln 6-16+2+12\ln2\n S_P=16-12\ln 6+12\ln 2\n S_P=16-12(\ln 6-\ln 2)\n\boxed{S_P=16-12\ln 3}

\displaystyle S_Q=\int\limits_2^6(12)/(x)\, dx\n S_Q=\left[12\ln x\right]_2^6\n S_Q=12\ln 6-12\ln 2\n S_Q=12(\ln6-\ln 2)\n \boxed{S_Q=12\ln 3}

\displaystyle V=\pi \int \limits_a^b f^2(x)\, dx\n\n V=\pi \int \limits_2^6 \left((12)/(x)\right)^2\, dx\n V=\pi \int \limits_2^6 (144)/(x^2)\, dx\n V=\pi\left[-(144)/(x)\right]_2^6\n V=\pi \cdot \left(-(144)/(6)-\left(-(144)/(2)\right)\right)\n V=\pi \cdot (-24+72)\n V=\pi \cdot48\n \boxed{V=48\pi}

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