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Home » Thus, the volume of the cone-shaped shell is \(\boxed27\pi\) cubic centimeters. - Get link 4share

Thus, the volume of the cone-shaped shell is \(\boxed27\pi\) cubic centimeters. - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Let $P = \mathbf{r}(t)$. The vector $\overrightarrow{CP} = \mathbf{r}(...
angle = \langle -1 + 3t, 4 - 2t, -5 + 3t
To minimize the distance, minimize $\|\overrightarrow{CP}\|^2$:
D^2 = (-1 + 3t)^2 + (4 - 2t)^2 + (-5 + 3t)^2
= (1 - 6t + 9t^2) + (16 - 16t + 4t^2) + (25 - 30t + 9t^2) \
= 42 - 52t + 22t^2
Take derivative and set to zero:
rac{d}{dt}(42 - 52t + 22t^2) = -52 + 44t = 0 \Rightarrow t = rac{13}{...
Substitute $t = rac{13}{11}$ into $\mathbf{r}(t)$:
P = \langle 1 + 3\cdotrac{13}{11}, 3 - 2\cdotrac{13}{11}, -2 + 3\cdo...

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