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[tex]inches^3[/tex] 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 = [tex]\frac{3}{2}[/tex] = 1.5 inches
Volume of the cone = [tex]\frac{1}{3} \pi r^2 h[/tex]
Substituting the values
Volume of smallcone = [tex]\frac{1}{3} \pi \times (1.5)^2 (3.5)[/tex]
=>[tex]\frac{1}{3} \pi \times (2.25)(3.5)[/tex]
=>[tex]\frac{1}{3} \pi \times (7.875)[/tex]
=>[tex]\frac{1}{3} \times 24.7275[/tex]
=>[tex]\frac{24.7275}{3}[/tex]
=>8.2425
Step 2 : Finding the volume of large cone
Radius = [tex]\frac{4.5}{2}[/tex] = 2.25 inches
Volume of the cone = [tex]\frac{4.5}{2}[/tex]
Substituting the values
Volume of largecone =[tex]\frac{1}{3} \pi \times (2.25)^2 (5.1)[/tex]
=>[tex]frac{1}{3} \pi \times (5.0625)(5.1)[/tex]
=>[tex]\frac{1}{3} \pi \times (21 .818)[/tex]
=>[tex]\frac{1}{3} \times (81.070)[/tex]
=>[tex]\frac{81.070}{3}[/tex]
=>27.02
Volume of large cone - volume of small cone
=>27.02 - 8.2425
=>18.77
=>19(rounding off to nearest tenth)
