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2 years ago

Find the volume of the figure

Mathematics

1 answer:

omeli [17]2 years ago

5 0

Answer:

1920 ft^3

Step-by-step explanation:

Split it in 2.

14*8*10 and 10*10*8

14*10*8 = 1120

10*10*8 = 800

800 + 1120 = 1920

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4vir4ik [10]

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1 year ago

What is 2 5/12 -(-2 1/6) Express the answer in simplest form.

VladimirAG [237]

Answer:
= 29/12 − -13/6

<span>= ((29 × 6) − (-13 × 12)) / (12 × 6) </span>

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2 years ago

there are 341 pine trees and spruce trees in woodlot. 122 trees were pine. what fraction of the trees were spruce?

Olenka [21]

Answer:

219 over 1000

Step-by-step explanation:

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2 years ago

A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

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2 years ago

A scale drawing of a patio is shown at right. The scale is 3 inches : 5.2 feet. What are the length and width of the patio? Find

ANTONII [103]

Answer:

The length is 5.2 and the width is 3 and the area is 15.6

Step-by-step explanation:

To get the area just multiply width by length

5 0

2 years ago

Read 2 more answers

Find the volume of the figure￼

Find the volume of the figure