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3 years ago

Find the VOLUME of this composite solid.

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

8 0

Answer:

(294π +448) cm³ ≈ 1371.6 cm³

Step-by-step explanation:

The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.

The cylinder volume is ...

V = πr²h = π(7 cm)²(6 cm) = 294π cm³

The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...

V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³

Then the total volume of the composite figure is ...

(294π +448) cm³ ≈ 1371.6 cm³

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0,8 cm on the map is equal to 8 m in real life

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3 years ago

What's the area please help?

alexgriva [62]

Answer:

48 units^2

Step-by-step explanation:

So i split the arrow to make it just one rectangle and one triangle

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3 years ago

Charlie bought 2 3/4 pounds of pears for $.76 per pound and 2 3/4 pounds of grapes for $1.40 per pound how much money in dollars

erma4kov [3.2K]

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5.94

Step-by-step explanation:

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8 0

3 years ago

Read 2 more answers

Mason takes his pulse. He counts 48 beats in 2/3 minute. Mason goes on a bike ride and takes his pulse again. Now he counts 81 b

Kazeer [188]

Answer:

Therefore, beats per minute did increase for 36.

Step-by-step explanation:

48: 2/3=x:1

48=2/3 × x

x=3/2×48

x=72

81:3/4=x:1

81=x×3/4

x=4/3×81

x=108

Therefore, beats per minute did increase for 36.

5 0

3 years ago

The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,

klasskru [66]

Given:

The scale factor is $s=\dfrac{1}{3}$ and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

$(x,y)\to (k(x-a)+a,k(y-b)+b)$

According to the given information, the scale factor is $\dfrac{1}{3}$ and the center of dilation is at (4,2).

$(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)$ ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

$C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)$

$C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)$

$C(-2,11)\to C'(-2+4,3+2)$

$C(-2,11)\to C'(2,5)$

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

$A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)$

From the given figure it is clear that the image of point A is (8,4).

$A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)$

On comparing both sides, we get

$\dfrac{1}{3}(m-4)+4=8$

$\dfrac{1}{3}(m-4)=8-4$

$(m-4)=3(4)$

$m=12+4$

$m=16$

And,

$\dfrac{1}{3}(n-2)+2=4$

$\dfrac{1}{3}(n-2)=4-2$

$(n-2)=3(2)$

$n=6+2$

$n=8$

Therefore, the coordinates of point A are (16,8).

5 0

3 years ago