Answer:
Step-by-step explanation:
Given is the hexagonal pyramid.
We know the radius of the base is same as its side.
<u>Find the base area:</u>
- A = 3√3/2a²
- A = 3√3/2*6² = 54√3
<u>Given the height and radius, find the side of the lateral triangular faces:</u>
Each of 6 triangles have sides 10, 10 and 6 units.
<u>Find the area using heron's formula:</u>
- s = P/2 = (10*2 + 6)/2 = 13
- s - a = s - b = 13 - 10 = 3
- s - c = 13 - 6 = 7
<u>Total surface area:</u>
Correct choice is B
Answer:
a) ⅓ units²
b) 4/15 pi units³
c) 2/3 pi units³
Step-by-step explanation:
4y = x²
2y = x
4y = (2y)²
4y = 4y²
4y² - 4y = 0
y(y-1) = 0
y = 0, 1
x = 0, 2
Area
Integrate: x²/4 - x/2
From 0 to 2
(x³/12 - x²/4)
(8/12 - 4/4) - 0
= -⅓
Area = ⅓
Volume:
Squares and then integrate
Integrate: [x²/4]² - [x/2]²
Integrate: x⁴/16 - x²/4
x⁵/80 - x³/12
Limits 0 to 2
(2⁵/80 - 2³/12) - 0
-4/15
Volume = 4/15 pi
About the x-axis
x² = 4y
x² = 4y²
Integrate the difference
Integrate: 4y² - 4y
4y³/3 - 2y²
Limits 0 to 1
(4/3 - 2) - 0
-2/3
Volume = ⅔ pi
There are 2 variables in this problem. One variable is the class number and other variable is the participation in extracurricular activities. Each variable has further two categories. There are two classes: Class 10 and 11. And students either participate or do not participate in extracurricular activities, which makes 2 categories.
The best approach to solve this question is to build a table and start entering the given information in it. When the given data has been entered fill the rest on basis of the data you have.
18 students from grade 11 participate in at least one Extracurricular activities. This means the rest students i.e. 22 students from grade 11 do not participate in Extracurricular activities.
32 students from grade 10 participate in at least one Extracurricular activities. This means total students who participate in at least one Extracurricular activities are 18 + 32 = 50 students.
The rest 50 students do not participate in at least one Extracurricular activities. From these 22 are from class 11. So the rest i.e. 28 are from class 10.
10(x-5)=-80
10x-50=-80
+50 +50
10x=-30
/10 /10
x=-3