Find the volume and surface area of the composite figure. Give your answer in terms of pi
PLS HELP
Answers
Given:
A diagram of a composite figure.
Radius of cone and hemisphere is 8 cm.
Height of the cone is 15 cm.
To find:
The volume and the surface area of the composite figure.
Solution:
Volume of a cone is:
[tex]V_1=\dfrac{1}{3}\pi r^2h[/tex]
Where, r is the radius and h is the height of the cone.
Putting [tex]r=8,h=15[/tex] in the above formula, we get
[tex]V_1=\dfrac{1}{3}\pi (8)^2(15)[/tex]
[tex]V_1=\pi (64)(5)[/tex]
[tex]V_1=320\pi[/tex]
Volume of the hemisphere is:
[tex]V_2=\dfrac{2}{3}\pi r^3[/tex]
Where, r is the radius.
Putting [tex]r=8[/tex], we get
[tex]V_2=\dfrac{2}{3}\pi (8)^3[/tex]
[tex]V_2=\dfrac{1024}{3}\pi [/tex]
[tex]V_2\approx 341.3\pi [/tex]
Now, the volume of the composite figure is:
[tex]V=V_1+V_2[/tex]
[tex]V=320\pi +341.3\pi[/tex]
[tex]V=661.3\pi[/tex]
The volume of the composite figure is 661.3π cm³.
The curved surface area of a cone is:
[tex]A_1=\pi r\sqrt{h^2+r^2}[/tex]
Where, r is the radius and h is the height of the cone.
Putting [tex]r=8,h=15[/tex] in the above formula, we get
[tex]A_1=\pi (8)\sqrt{(15)^2+(8)^2}[/tex]
[tex]A_1=\pi (8)\sqrt{289}[/tex]
[tex]A_1=\pi (8)(17)[/tex]
[tex]A_1=136 \pi [/tex]
The curved surface area of the hemisphere is:
[tex]A_2=2\pi r^2[/tex]
Where, r is the radius.
Putting [tex]r=8[/tex], we get
[tex]A_2=2\pi (8)^2[/tex]
[tex]A_2=2\pi (64)[/tex]
[tex]A_2=128\pi [/tex]
Total surface area of the composite figure is:
[tex]A=A_1+A_2[/tex]
[tex]A=136\pi +128\pi[/tex]
[tex]A=264\pi[/tex]
The total surface area of the composite figure is 264π cm².
Therefore, the correct option is A.
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Step-by-step explanation:
0 = pi/3 radians. Identify the terminal point and tan 0.
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The terminal point is (0.5, 0.866), and the value of the tangent is 0.173.
How to identify the terminal point?For any angle a, the coordinates of the terminal point are given by:
x = cos(a)
y = sin(a).
In this case, the angle is a = pi/3
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
bi
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Answer:
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Answers
=============================================================
Explanation
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
6 x 7 =42
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2, 3, 6
Step-by-step explanation:
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C, E, F,
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Sum of any pentagon is 540°.
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150
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Explained already by another user
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Step-by-step explanation:
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