Answer:
(A)
Step-by-step explanation:
To Simplify: The quantity 3 times x to the 4th power plus 5 times x to the 2nd power plus 2 times x all over x.
Solution: The given statement can be easily rewritten as:
,
and
Thus, according to the statement, the expression can be written as:
⇒
which is the required simplified expression.
Thus,option A is correct.
Answer:
The correct answer is:
The volume of the triangular prism is equal to the volume of the cylinder
Step-by-step explanation:
Given that there are two figures
1. A right triangular prism and
2. Right cylinder
Area of cross section of prism is equal to Area of cross section of cylinder.
Let this value be <em>A</em>.
Also given that Height of prism = Height of cylinder = <em>6</em>
Volume of a prism is given as:
Cross section of cylinder is a circle.
<em>Area of circle</em> is given as:
Area of cross section, A =
Volume of cylinder is given as:
From equations (1) and (2) we can see that
Hence, the correct answer is:
Volume of prism is equal to the volume of cylinder.
Answer:
1) The volume of the frustum is 27·(√3)·h
2) The surface area the frustum is 24·h + 54·√3
Step-by-step explanation:
1) A frustum of the regular triangular prism is a portion of the triangular prism
The length of the edge of the triangle prism = 12
The area of the triangular face, A = (√3/4)·a²
∴ A = (√3/4)·12² = 36·√3
When
The volume of the triangular prism, V = A·h = (36·√3)·h
By triangle proportionality theorem, the cross sectional area of the top half of the triangular prism = (√3/4)·6² = 9·(√3)
The volume of the top half, V₂ = 9·(√3)·h
The volume of the frustum = V - V₂ = (36·√3)·h - 9·(√3)·h = 27·(√3)·h
The volume of the frustum = 27·(√3)·h
2) The surface area of the triangular side of the frustum is given as follows;
A = 36·√3- 9·(√3) = 27·(√3)
The surface area the frustum, = 2×27·(√3) + 2 ×6 ×h + 12×h = 24·h + 54·√3
The surface area the frustum = 24·h + 54·√3