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3 years ago

According to Cavalieri’s Principle, if a cone and a pyramid have the same height, which of the following answer choices is true?

Mathematics

1 answer:

Contact [7]3 years ago

8 0

Answer:

Option (C).

Step-by-step explanation:

If a cone and a pyramid have same height,

Volume of a cone = $\frac{1}{3}(\text{Area of the base})\times (\text{height}))$

= $\frac{1}{3}(A_{1})\times (h)$

Volume of a pyramid = $\frac{1}{3}(\text{Area of the base})\times (\text{height})$

= $\frac{1}{3}(A_{2})(h)$

As we can see if area of the bases of cone and pyramid are same, their volumes will be same.

Cavalier's Principle states, two solids having same heights and all cross sections of equal areas at the equal distances from the base, will have the same volumes.

Therefore, as per Cavalier's Principle, option (C) will be the answer.

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What is the area of the triangle?

ArbitrLikvidat [17]

9514 1404 393

Answer:

7 square units

Step-by-step explanation:

There are several ways the area of triangle EBD can be found.

find the lengths EB, BD, DE and use Heron's formula (messy due to roots of roots being involved).
define point G at the lower left corner and subtract the areas of ∆DEG and BCD from trapezoid BCGE.
figure the area from the coordinates of the vertices.
use Pick's theorem and count the dots.

We choose the latter.

Pick's theorem says the area of a polygon can be found as ...

A = i + b/2 -1

where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.

The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...

A = 6 + (4/2) -1 = 7

The area of ∆EBD is 7 square units.

4 0

3 years ago

I need some help ASSAPPP please

Sedaia [141]

I cant see it sorry :(

8 0

3 years ago

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Factor the following:<br><br> 5∙(a+3)^2-(a+3)

Zanzabum

Answer:

(a+3)(5a+14)

Step-by-step explanation:

Factor the polynomial.

(a+3)(5a+14)

3 0

3 years ago

Find the max and min values of f(x,y,z)=x+y-z on the sphere x^2+y^2+z^2=81

Anton [14]

Using Lagrange multipliers, we have the Lagrangian

$L(x,y,z,\lambda)=x+y-z+\lambda(x^2+y^2+z^2-81)$

with partial derivatives (set equal to 0)

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$
$L_y=1+2\lambda y=0\implies y=-\dfrac1{2\lambda}$
$L_z=-1+2\lambda z=0\implies z=\dfrac1{2\lambda}$
$L_\lambda=x^2+y^2+z^2-81=0\implies x^2+y^2+z^2=81$

Substituting the first three equations into the fourth allows us to solve for $\lambda$ :

$x^2+y^2+z^2=\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}=81\implies\lambda=\pm\dfrac1{6\sqrt3}$

For each possible value of $\lambda$ , we get two corresponding critical points at $(\mp3\sqrt3,\mp3\sqrt3,\pm3\sqrt3)$ .

At these points, respectively, we get a maximum value of $f(3\sqrt3,3\sqrt3,-3\sqrt3)=9\sqrt3$ and a minimum value of $f(-3\sqrt3,-3\sqrt3,3\sqrt3)=-9\sqrt3$ .

5 0

3 years ago

What is the diameter of a circular field whose area is 616cm^2<br><br>

Oksana_A [137]

Answer:

Step-by-step explanation:

$d=2\sqrt{\frac{A}{\pi}} =2\sqrt{\frac{616}{\pi} }$ ≈ $28.00563cm$

rounding 28.00563 to 28.

So hence, your answer is 28cm

-------------------------------------------------------------------------------------------------------------The beautiful thing about learning is that no one can take it away from you!

B.B.King

Thanks!

Have a great day!

~ms115~

3 0

2 years ago

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