Water, in a $4-\text{in.}$ diameter jet with speed of $100\ \mathrm{ft} / \mathrm{s}$ to the right, is deflected by a cone that moves to the left at $45\ \mathrm{ft} / \mathrm{s}$. Determine (a) the thickness of the jet sheet at a radius of $9\ \text{in.}$ and (b) the external horizontal force needed to move the cone.

How can you rewrite the formula for the volume of a cone using the diameter d instead of the radius r?

Which three-dimensional figure does NOT have a base? A. cone B. prism C. pyramid D. sphere

Find a parametrization of the surface. The portion of the cone

$$z = 2 \sqrt { x ^ { 2 } + y ^ { 2 } }$$

between the planes z = 2 and z = 4.

In this problem, you will derive the formula for the volume of a right circular cone with height $l$ and base radius $b$ by rotating the line $y = ax$ from $x = 0$ to $x = l$ around the $x$-axis. See Figure $8.111.$

(a) What value should you choose for $a$ such that the cone will have height $l$ and base radius $b?$

You know the volume of a cylinder. How can you find the volume of a cone with the same base and height?

Find the radius of a right cone with slant height 21 m and surface area $232 \pi \mathrm{m}^{2}$.

What is the surface area of the given cone, whose altitude is 5 feet and has a diameter of 4 feet?

Find the volume to the nearest whole number.

Given: a cone with a height of 7.1 ft and a radius of 5 ft

Find the volume of the region lying above the cone

$$\phi = \phi _ { 0 }$$

and below the sphere

$$\rho = R.$$

The height of a sample cone from a production line is measured as 11.4 cm, while the radius is measured as 2.9 cm. Each of these measurements could be off by 0.2 cm. Approximate the maximum possible error in the volume of the cone.

Find the volume of an oblique cone with a height of $10.5$ millimeters and a radius of $1.6$ millimeters. Round to the nearest tenth.

The radius of the base of the right circular cone shown below is 5 inches, and the height of the cone 7 inches. Solving which of the following equations gives the measure, $\theta$, of the angle formed by the slant height of the cone and a radius? F. $\tan\theta=\frac{5}{7}$ G. $\tan\theta=\frac{7}{5}$ H. $\sin\theta=\frac{5}{7}$ J. $\sin\theta=\frac{7}{5}$ K. $\cos\theta=\frac{7}{5}$

$y=2-2 x, y=0,$ and $x=0 ;$ about the $x$-axis Verify that your answer agrees with the volume formula for a cone.)