The volume of a sphere, given its radius, is 

$\displaystyle V = \frac{4\pi r^{3}}{3}$

Set $\displaystyle V = 1,000$, solve for $\displaystyle r$, and double that to get the diameter.

$\displaystyle 1,000= \frac{4\pi r^{3}}{3}$

$\displaystyle r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$\displaystyle r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

The diameter of a sphere is $\displaystyle 6t$ so the radius of the sphere would be $\displaystyle 6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$\displaystyle Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3$ 

The volume enclosed by a sphere is given by the formula:

$\displaystyle Volume=\frac{4}{3}\pi r^3$

where $\displaystyle r$ is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $\displaystyle 10\div 2=5$ meters. Now we can get:

$\displaystyle Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times 5^3=\frac{4}{3}\times \pi \times 125\approx 523.6 m^3$

The volume of a sphere is:

$\displaystyle Volume=\frac{4}{3}\pi r^3$

Where $\displaystyle r$ is the radius of the sphere. We know the volume and can solve the formula for $\displaystyle r$:

$\displaystyle Volume=\frac{4}{3}\pi r^3=1000\Rightarrow r^3=\frac{3\times1000 }{4\pi}\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$\displaystyle Diameter=2r=2\times 6.2=12.4inches$

To find the volume of a sphere, use the following formula:

$\displaystyle \text{Volume}=\frac{4}{3}\pi\times r^3$, where $\displaystyle r$ is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$\displaystyle r=10\div2=5$ $\displaystyle in$

Now, plug this value into the volume equation.

$\displaystyle \text{Volume}=\frac{4}{3}\pi\times 5^3$

$\displaystyle \text{Volume}=\frac{4}{3}\pi\times 125$

$\displaystyle \text{Volume}=\frac{500}{3}\pi=523.6$ $\displaystyle in^3$ 

Write the formula for the volume of the sphere.

$\displaystyle V=\frac{4}{3}\pi r^3$

The radius is half the diameter, which is five.  Substitute the value.

$\displaystyle V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125)= \frac{500}{3}\pi$

The radius of the sphere is half the diameter, or 6 feet; use the formula

$\displaystyle V= \frac{4}{3} \pi r^{3}$ .

Setting $\displaystyle r=6$:

 $\displaystyle V= \frac{4}{3} \pi \cdot 6^{3} \approx904.8 ft^{3}$

First, convert the dimensions to cubic centimeters by multiplying by $\displaystyle 100$: the cone has height $\displaystyle 300cm$, and its base has radius $\displaystyle 200cm$.

$\displaystyle 3m*\frac{100cm}{1m}=300cm\ \ \2m*\frac{100cm}{1m}=200cm$

Its volume is found by using the formula and the converted height and radius.

$\displaystyle V=\frac{1}{3} \pi r^{2}h$

$\displaystyle V=\frac{1}{3} \pi (200cm)^{2} ( 300cm )\approx 12,566,371 \; \textrm{cm}^{3}$

Now multiply this by $\displaystyle 0.45\frac{g}{cm^3}$ to get the mass.

$\displaystyle m=V*\rho$

$\displaystyle 12,566,371cm^3*0.45\frac{g}{cm^3} \approx 5,654,867g$

Finally, convert the answer to kilograms.

$\displaystyle 5654867g *\frac{1kg}{1,000g} \approx 5,655kg$

The volume of a cone is:

$\displaystyle Volume=\frac{1}{3}\pi r^2h$

where $\displaystyle r$ is the radius of the circular base, and $\displaystyle h$ is the height (the perpendicular distance from the base to the vertex).

As the circular base area is $\displaystyle \pi r^2$, so we can rewrite the volume formula as follows:

$\displaystyle Volume =\frac{A\times h}{3}$

where $\displaystyle A$ is the circular base area and known in this problem. So we can write:

$\displaystyle Volume =\frac{A\times h}{3}=\frac{4\times 4}{3}=\frac{16}{3}\approx 5.333 m^3$

We know that density is defined as mass per unit volume or:

$\displaystyle \rho =\frac{m}{v}$

Where $\displaystyle \rho$ is the density; $\displaystyle m$ is the mass and $\displaystyle v$ is the volume. So we get:

$\displaystyle m=\rho v=1000\times 5.333=5333 Kg$

The volume of a cone is:

$\displaystyle Volume=\frac{1}3{}\pi r^2h$

where $\displaystyle r$ is the radius of the circular base, and $\displaystyle h$ is the height (the perpendicular distance from the base to the vertex).

$\displaystyle Volume=\frac{1}3{}\pi r^2h =\frac{1}3{}\pi t^2\times 2t=\frac{2}{3}\pi t^3$