All categories

2 years ago

Explain how Cavalieri’s principle can be used to find the volume of any solid.

Mathematics

1 answer:

Kruka [31]2 years ago

8 0

Answer:

Cavalier's principle can be used to find the volume of any solid.

Step-by-step explanation:

Cavalier's Principle:

Cavalier introduced parallel planes and area to describe the relationship between solids.
Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.

Suppose two regions are included between two parallel planes.
If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
The formula for the volume of a prism is the area of the base times the height.

You might be interested in

What is the solution to the equation below ?

irina [24]

7/8(x-1/2)= -49/80

Multiply the bracket by 7/8

7/8x-7/16= -49/80

Move -7/16 to other side. Sign changes from -7/16 to +7/16

7/8x-7/16+7/16= -49/80+7/16

7/8x= -49/80+7/16

Find common denominator for 7/16 which is 5. Multiply 5 for the numerator and denominator.

7(5) / 16 (5)

= 35/80

7/8x= -49/80+35/80

7/8x= -14/80

Reduce -14/80 , divide by 2

(-14) /2=7 , 80/2= 40

-14/80= -7/40

7/8x= -7/40

Multiply by 8/7

7/8x*8/7= -7/40 * 8/7

Cross out 7 and 7 , and divide by 7. Cross out -7 and 7 and divide by 7. Cross out 40 and 8 divide by 8.

x= -1/5

Answer: x= -1/5 - G.

3 0

3 years ago

Find the volume of a half sphere with a radius of 10

Ugo [173]

The volume of a sphere is calculated like so:
v = 4*pi*r^3/3
so half sphere will have half that volume:
v = (4*pi*r^3/3)(1/2)
v = 4*pi*r^3/6
plug in the data:
v = 4*pi*(10)^3/6
v = 2094.4
that is the volume of the half sphere

7 0

2 years ago

Triangle ABC has coordinates of A(–8, –8), B(4, –2), and C(2, 2). Find the coordinates of its image after a dilation centered at

kherson [118]

The answer is (C) because you multiply each point by 1.5.

7 0

2 years ago

Read 2 more answers

When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected

jasenka [17]

Answer:

A. Initially, there were 12 deer.

B. N(10) corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. After 15 years, there will be 410 deer.

D. The deer population incresed by 30 specimens.

Step-by-step explanation:

$N=\frac{12.36}{0.03+0.55^t}$

The amount of deer that were initally in the reserve corresponds to the value of N when t=0

$N=\frac{12.36}{0.33+0.55^0}$

$N=\frac{12.36}{0.03+1} =\frac{12.36}{1.03} = 12$

A. Initially, there were 12 deer.

B. $N(10)=\frac{12.36}{0.03 + 0.55^t} =\frac{12.36}{0.03 + 0.0025}=\frac{12.36}{y}=380$

B. N(10) corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. $N(15)=\frac{12.36}{0.03+0.55^15}=\frac{12.36}{0.03 + 0.00013}=\frac{12.36}{0.03013}= 410$

C. After 15 years, there will be 410 deer.

D. The variation on the amount of deer from the 10th year to the 15th year is given by the next expression:

ΔN=N(15)-N(10)

ΔN=410 deer - 380 deer

ΔN= 30 deer.

D. The deer population incresed by 30 specimens.

8 0

2 years ago

Find the equation of the line parallel to the line y = 4x – 2 that passes through the point (–1, 5).

Anni [7]

Find the equation of the line parallel to the line y = 4x – 2 that passes through the point (–1, 5).

y = 4x – 2 has slope = 4
parallel lines have same slope so slope = 4

passes through the point (–1, 5).
y = mx+b
5 = 4(-1) + b
b =9

equation
y = 4x + 9

answer

The slope of y = 4x – 2 is 4
The slope of a line parallel to y = 4x – 2 is 4
The equation of the line parallel to y = 4x – 2 that passes through the point (–1, 5) is y = 4x + 9

4 0

3 years ago

Read 2 more answers