All categories

3 years ago

Find the best approximation of the volume of the sphere.

Mathematics

1 answer:

BabaBlast [244]3 years ago

5 0

V = 4/3πr³
V = 4/3(3.14)(14)³
V = 4/3(3.14)(2744)
V = 4/3(8616.16)
V = 11488.21333cm³

You might be interested in

1: 2(y+6)=?<br> 2: 6-(-6+2)=?<br> What is the property of equation?

Citrus2011 [14]

1: 2y+12

2: 6 +6 -2
+12 -2
= 10

5 0

3 years ago

Janet's car will go 462 miles on 16.5 gallons of gas. How many miles will it take to drive 2719 miles

ololo11 [35]

2719/462 x 16.5 = 97.10714gallons which is approximately 97 gallons.

7 0

2 years ago

What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides $12-2x$ and $16-2x$ , and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

$(12-2x)(16-2x)x = 4x^3-56x^2+192x$

The derivative of this function is

$12x^2-112x+192$

and it equals zero if and only if

$12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}$

If we evaluate the volume function at these points, we have

$f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)$

So, the maximum volume is given if you cut a square with side length

$x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7$

5 0

2 years ago

The weight W of an aluminum flatboat varies directly with the length L of the boat. If a 6-foot boat weighs 102 pounds, then w

AnnZ [28]

Answer:

The 11 foot boat ways 187 pounds

Step-by-step explanation:

102 / 6 = 17

17 * 11 = 187

3 0

2 years ago

The value of a jewel in 2015 was $17500. The jewel was purchased in 2008, and its value appreciated 2.5%

ArbitrLikvidat [17]

Answer:

$14722.14

Step-by-step explanation:

We are given that

In 2015

The value of jewel=$17500

Rate of appreciation, r=2.5%

We have to find the initial value of the jewel when it was first bought.

Time, n=7 years

Final value= $Initial\;value (r/100+1)^n$

Using the formula

$17500=Initial\;value(2.5/100+1)^7$

$17500=Initial\;value(1.025)^7$

$Initial\;value=\frac{17500}{(1.025)^7}$

Initial value=$14722.14

Hence, the the initial value of the jewel when it was first bought=$14722.14

5 0

2 years ago