Question

Find the volume of the oblique cone A 1206.4 inB 402.1 in.C 301.6D 100.5 in.

Answer 1

D. 100.5 cubic inches

Step-by-step explanation

Step 1

the volume of an oblique cone is given by:

`v=(1)/(3)\cdot\pi\cdot r^2\cdot h`

then, let

h=6

radius = unknown= r

Step 2

find the radius

we have a right triangle

where

hypotenuse(black)= 10

angle(yellow) =x

adjacent side(green)=6

opposite side = diameter(purple)

diameter = 2 * radius=opposite side

then,

radius(purple)=(diameter/2)

use the Pythagoras Theorem to find diameter

`\begin{gathered} P\mathrm{}T. \\ \text{opposite side}^2+adjacentside^2=hypotenuse^2 \\ \text{replace} \\ \text{diameter}^2+(6in)^2=(10in)^2 \\ isolate\text{ diameter} \\ diameter^2=(10in)^2-(6in)^2 \\ diameter^2=100in^2-36in^2 \\ diameter^2=64in^2 \\ \sqrt[]{diameter^2}=\sqrt[]{64in^2} \\ \text{diameter}=\text{ 8 inches} \end{gathered}`

so, diameter is 8 inches

Step 3

using the diameter, find the radius

`\begin{gathered} \text{radius}=\text{ }(diameter)/(2) \\ \text{radius}=\frac{8\text{ inches}}{2} \\ \text{radius = 4 inches} \end{gathered}`

Step 4

finally, replace the values for h and r in the volume formula

`\begin{gathered} v=(1)/(3)\cdot\pi\cdot r^2\cdot h \\ v=(1)/(3)\cdot\pi\cdot(4)^2\cdot6 \\ v=(1)/(3)\cdot\pi\cdot16\cdot6 \\ v=32\pi \\ v=100.530 \\ \end{gathered}`

so, the answer is D. 100.5 cubic inches