The radius and height of a right circular con | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the radius $r = 3x$ and the height $h = 4x$.The volume of a right circular cone is given by $V = \frac{1}{3}\pi r^2 h$.Substituting the given

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Let the radius $r = 3x$ and the height $h = 4x$.The volume of a right circular cone is given by $V = \frac{1}{3}\pi r^2 h$.Substituting the given values: $96\pi = \frac{1}{3}\pi (3x)^2 (4x)$.Simplifying the equation: $96\pi = \frac{1}{3}\pi (9x^2)(4x) = 12\pi x^3$.Dividing both sides by $12\pi$: $x^3 = \frac{96}{12} = 8$.Taking the cube root: $x = 2$.Thus,the radius $r = 3(2) = 6\, cm$ and the height $h = 4(2) = 8\, cm$.The slant height $l$ is given by $l = \sqrt{r^2 + h^2}$.$l = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\, cm$.

The radius and height of a right circular cone are in the ratio $3: 4$. If its volume is $96\pi\, cm^3$,what is its slant height (in $cm$)?

Similar Questions

$A$ reservoir, $30\, m$ long and $15\, m$ broad, is filled with water. How many gallons of water must be taken out to lower the level of water by $4\, m$? (in gallons)

Assume that a drop of water is spherical and its diameter is $\frac{1}{10} \text{ cm}$. $A$ conical glass has a height equal to the diameter of its rim. If $32,000$ drops of water fill the glass completely,then the height of the glass (in $\text{cm}$) is:

$A$ well of $11.2 \, m$ diameter is dug $8 \, m$ deep. The earth taken out has been spread all around it to a width of $7 \, m$ to form a circular embankment. Find the height of the embankment in meters.

How many cubes of $10\, cm$ edge can be put in a cubical box of $1\, m$ edge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module