Question

A company makes two different sized ice cream cones the smaller cone 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

Answer 1

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 nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone?

Answer:

The volume of the larger cone is 19$inches^3$ greater than the volume of the smaller cone

Step-by-step explanation:

Given:

Length of small cone = 3.5 inches

Diameter of small cone = 3 inches

Length of large cone = 5.1 inches

Diameter of large cone = 4.5 inches

To Find :

how much greater is the volume of the larger cone than the volume of the smaller cone = ?

Solution:

Step 1 : Finding the volume of small cone

Radius = $\frac{3}{2}$ = 1.5 inches

Volume of the cone  = $\frac{1}{3} \pi r^2 h$

Substituting the values

Volume of smallcone = $\frac{1}{3} \pi \times (1.5)^2 (3.5)$

=>$\frac{1}{3} \pi \times (2.25)(3.5)$

=>$\frac{1}{3} \pi \times (7.875)$

=>$\frac{1}{3} \times 24.7275$

=>$\frac{24.7275}{3}$

=>8.2425

Step 2 : Finding the volume of large cone

Radius = $\frac{4.5}{2}$ = 2.25 inches

Volume of the cone  = $\frac{4.5}{2}$

Substituting the values

Volume of largecone =$\frac{1}{3} \pi \times (2.25)^2 (5.1)$

=>$frac{1}{3} \pi \times (5.0625)(5.1)$

=>$\frac{1}{3} \pi \times (21 .818)$

=>$\frac{1}{3} \times (81.070)$

=>$\frac{81.070}{3}$

=>27.02

Volume of large cone - volume of small cone

=>27.02 -  8.2425

=>18.77

=>19(rounding off to nearest tenth)