Question

A company makes two different-sized ice cream cones. The smaller cones are 3.5 inches tall and have a diameter of 3 inches. The larger cones are 5.1 inches tall and have a diameter of 4.5 inches. Abour how much greater, to the mearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone?
Show your work.
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Answer 1

Answer:

The volume of the larger cone is 18.8 sq.inches more than the volume of the smaller cone.

Step-by-step explanation:

Height of smaller cone = 3.5 inches

Diameter of smaller cone = 3 inches

Radius of smaller cone = $\frac{3}{2} = 1.5 inches$

Volume of smaller cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 1.5^2 \times 3.5=8.25 inches ^2$

Height of larger cone = 5.1 inches

Diameter of larger cone = 4.5 inches

Radius of larger cone =$\frac{4.5}{2}=2.25 inches$

Volume of larger cone =$\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 2.25^2 \times 5.1 =27.048 inches^2$

Difference in volumes = 27.048-8.25=$18.798 inches^2$

Difference in volumes to nearest tenth =$18.8 inches^2$

So, the volume of the larger cone is 18.8 sq.inches more than the volume of the smaller cone.

Answer 2

Answer:

The Volume of large cone is  19.545 $inches^3$ greater than the smaller cone

Step-by-step explanation:

Given:

Size of the small cone =  3.5 inches

Diameter of the small cone  = 3 inches

Size of the large cone =  3.5 inches

Diameter of the small cone  = 3 inches

To Find:

How much greater, to the nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone = ?

Solution:

Volume of the small cone :

Radius = $\frac{diameter}{2}$

Radius = $\frac{3}{2}$

Radius = 1.5 inches

volume of the cone  =$\pi rl$

substituting the values,

=>$\pi (1.5)(3.5)$

=>$\pi(5.25)$

=> 16.485 $inches^3$

Volume of the large cone :

Volume of the large cone :

Radius = $\frac{diameter}{2}$

Radius = $\frac{4.5}{2}$

Radius = 2.25 inches

volume of the cone  =$\pi rl$

substituting the values,

=>$\pi (2.25)(5.1)$

=>$\pi(11.475)$

=>36.06 $inches^3$

Now ,

volume of small cone - volume of large cone

=>36.06 - 16.485

=>19.545 $inches^3$