Respuesta :
The volume of the given cone is; Option D: 136.1 in³
We are given;
Radius of cone; r = 5.1 inches
Height of cone; h = 5 inches
π = 3.14
Formula for volume of cone is;
V = ¹/₃πr²h
Plugging in the relevant values gives;
V = ¹/₃ * 3.14 * 5.1² * 5
V = 136.119 in³
Approximating to the nearest tenth gives;
V = 136.1 in³
Read more about volume of a cone at; https://brainly.com/question/11576719
Answer:
The correct answer is obtion b) 136.1 in³.
Step-by-step explanation:
Given :
- »» Radius of cone = 5.1 in
- »» Height of cone = 5 in
To Find :
- »» Volume of cone
Using Formula :
[tex]{\star{\small{\underline{\boxed{\sf{\red{Volume_{(Cone)} = \dfrac{1}{3}\pi {r}^{2}h}}}}}}}[/tex]
- ✧ π = 3.14
- ✧ r = radius
- ✧ h = height
Solution :
Substituting all the given values in the formula to find volume of cone :
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3}\pi {r}^{2}h}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times (5.1)^{2} \times 5}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times (5.1 \times 5.1)\times 5}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times (26.01)\times 5}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3} \times 3.14 \times 26.01\times 5}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1}{3} \times \dfrac{314}{100} \times \dfrac{2601}{100} \times 5}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{1 \times 314 \times 2601 \times 5}{100 \times 100 \times 3}}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{ 314 \times 13005}{100 \times 300}}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} = \dfrac{4083570}{30000}}}}}}[/tex]
[tex]{\longrightarrow{\small{\sf{\purple{Volume_{(Cone)} \approx 136.1 \: {in}^{3}}}}}}[/tex]
[tex]\star{\small{\underline{ \boxed{\frak{\pink{Volume_{(Cone)} \approx 136.1 \: {in}^{3}}}}}}}[/tex]
Hence, the volume of cone is 136.1 in³.
[tex]\rule{300}{1.5}[/tex]
