Consider the figures shown to answer Part A and Parts B.

A series of three? separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers. Each

Nadya [2.5K]

Answer:

$312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$

Step-by-step explanation:

We have been given that a series of 3 separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers.

Each of the three tunnels is shaped like a half-cylinder with a radius of 5 meters.

Since we know that volume of a semicircular or a half cylinder is half the volume of a circular cylinder.

$\text{Volume of a semicircular cylinder}=\frac{\pi r^2h}{2}$ , where,

r = Radius of cylinder,

h = height of the cylinder.

Upon substituting our given values in volume formula we will get,

$\text{Volume of a semicircular cylinder}=\frac{\pi (5\text{ km})^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*25\text{ km}^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*625\text{ km}^3}{2}$

$\text{Volume of a semicircular cylinder}=\pi*312.5\text{ km}^3$

$\text{Volume of a semicircular cylinder}=981.74770\text{ km}^3$

Therefore, the volume of earth removed to build the three tunnels is $312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$ .

4 0

3 years ago

In a forested area, the number of trees, T can be expressed as a function of the initial number of trees planted. If the initial

Wewaii [24]

N = N (1+0.20)^5
o

Here, that'd be 10000(1.20)^5, or 24883 trees.

7 0

2 years ago

if Ingles 2 and 14 are congruent then line T and then you are parallel what is the theorem to this question

Nostrana [21]

Answer:

lol na im good

Step-by-step explanation:

7 0

3 years ago

Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx

Alex787 [66]

Answer:

Step-by-step explanation:

we have

$cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.$