Volume of cone is 132cm^3.Height is 11 more than radius. Find the radius and height.?

Question

Take pi as twenty two divided by seven i,e, take ∏ as 22/7

Answer 1

Please note that 22/7 is a close approximation of pi, but it is not the exact value. The exact value of pi is an irrational number, meaning that it cannot be expressed as a fraction of two integers. However, 22/7 is a good approximation for most practical purposes.

Answer 2

Pi value is not fixed. 22/7 is an approx value of pi.if we need any thing pure answer we need the exact value . Without exact values we can't find but we try by 22/7

Answer 3

Haha, you're being clever! However, that's not the correct value of pi. Pi is actually an irrational number, meaning that it can't be written as a fraction. The decimal value of pi continues on forever, and does not repeat. In fact, the first one million digits of pi have been calculated! So, while you can take an approximation of pi as 22/7, that's not the true value of this famous mathematical constant.

Answer 4

Volume of cone = 1/3pir^2h 

Take pi as 22/7

132cm^3=1/3×22/7×r^2×11

132cm^3 = 242r^2/21

Cross multiply then you have 

r^2 =2772cm^3/242

The result is 11.45

To get your radius, transfer the power of 2 to the other side which changes to square root. 

r=√11.45

r=3.38cm

Answer 5

To find the radius and height of the cone, we can use the formula for the volume of a cone, which is given by: 

            V= pie*r^2h/3

            where:

            V is the volume of the cone(132cm^3 is this case)

            pie is approximately 22/7

            r is the radius of the base of the cone, and 

            h is the height of the cone.

As mentioned that the height is 11 more than the radius, so h=r+11.

now , plug in the values into the formula:

                                                             132=22*r^2(r+11)/3*7

                                                              2772=22*r^2(r+11)

                                                              r^2(r+11)=126

After solving a cubic equation we get r=3

so h=r+11=3+11=14cm 

Therefore radius is 3cm and height is 14cm

Answer 6

lets radius of cone be x.

so height of cone is x+11.

volume of cone as given=132cm^3

volume of  cone=1/3*pi*r^2*h

so put all values in equation

132=1/3*22/7*r^2*(r+11)

divide by 1/3 on both side  we get

396=pi*r^2*(r+11)

 pi=22/7

2772=22*r^2(r+11)

126=r^3+11r^2

on solving this equation by cubic method

we get r=3

so height=11+3=14cm

and radius =3cm. 

Answer 7

Volume = (II*r^2)*h/3

Assuming pi as the given value which is not very accurate and putting volume as 132 and h= r+11 we get

     132 = (22/7)(r^2)(r+11)/3

  6*7*3 = r^3 + 11r^2

   r^3 + 11r^2 + 126=0

 solving this equation we get ! negative and 2 unreal roots. Hence, a cone of these dimensions can't exist.

   

Answer 8

Let's denote the radius of the cone as \( r \) and the height as \( h \). The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3} \pi r^2 h \).

Given that the volume is \( 132 \, \text{cm}^3 \), and the height is \( 11 \) more than the radius (\( h = r + 11 \)), we can set up the equation:

\[ 132 = \frac{1}{3} \pi r^2 (r + 11) \]

Solving this equation will give us the values of \( r \) and \( h \). Please note that the exact values involve \(\pi\) and might not be nice whole numbers.