Question

The radius and perpendicular height of a cone are in the ratio 5:12 if the volume of the cone is 314m cubic, find its perpendicular height and the slant height.​

Answer 1

Answer:

Perpendicular height = 12 metre

Slant height = 5 metre.

Step-by-step explanation:

Solution is given in figure.

Answer 2

Answer:

Given:-

The radius and perpendicular height of a cone are in the ratio 5 : 12. If the volume of the cone is 314m³, find its perpendicular height and the slant height.

To Find:-

The perpendicular height and the slant height.

Note:-

●》Here, we will find perpendicular height by Volume of cone formula i.e $Volume \ \ of \ \ cone = \dfrac{1}{3} × π × r² × h$; whereas r = radius, h = perpendicular height, π = 3.14

●》After finding perpendicular height, we will find slant height by its formula i.e. $l² = r² + h²$; whereas l = slant height, r = radius, h = perpendicular height.

●》Transposing is also required during solution, it is a process in which we change the side of known value for finding unknown value and in this process signs are also changed. For example - Postive signs becomes Negative signs, Multiple signs becomes Divisional signs, cube becomes cube root, Square becomes under root.

Solution:-

[ First, finding perpendicular height ]

$\huge\red{Volume \ \ of \ \ cone = 314m}$

$\huge\red{Radius \ \ and \ \ Perpendicular \ \ height = 5 : 12}$

$\huge\red{ \ \ Their \ \ Actual \ \ value = ?, Let \ \ them = x}$

☆ According to note first point ( radius will be = 5x, perpendicular height will be = 12x )~

▪︎$Volume \ \ of \ \ cone = \dfrac{1}{3} × π × r² × h$

▪︎$314m³ = \dfrac{1}{3} × 3.14 × ( 5x )² × 12x$

▪︎$314m³ = \dfrac{3.14}{3} × 25x² × 12x$

▪︎$314m³ = \dfrac{3.14}{3} × 300x³$

▪︎$314m³ = \dfrac{942}{3}x³$

☆ According to note second point ( Transposing )~

▪︎$314m³ × 3 = 942x³$

▪︎$942m³ = 942x³$

▪︎$\cancel\dfrac{942m³}{942} = x³$

▪︎$1m³ = x³$

▪︎$³\sqrt 1m³ = x$

▪︎$³\sqrt 1m × 1m × 1m = x$

▪︎$1m = x$

▪︎$\huge\pink{Perpendicular \ \ height = 12x = 12 × 1m => 12m}$

$\huge\pink{Radius = 5x = 5 × 1m => 5m}$

__________________________________________________

[ Now, we will find slant height ]

$\huge\red{r = 5m, h = 12m}$

$\huge\red{ \ \ \ \ Slant \ \ height = ?}$

☆ According to note second point~

▪︎$l² = r² + h²$

▪︎$l² = ( 5m )² + ( 12m )²$

▪︎$l² = 25m² + 144m²$

▪︎$l² = 169m²$

☆ Transposing square to other side~

▪︎$l = \sqrt 169m²$

▪︎$l = \sqrt 13m × 13m$

☆ After taking pairs in one~

▪︎$l = 13m$

$\huge\pink{Slant \ \ height => l = 13m}$

Answer:-

Hence, the perpendicular height = 12m.

• Slant height = 13m.

:)