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mr Goodwill [35]
3 years ago
8

tom has a cube a rectangular prism and a triangular prism. which of the shapes have more than 6 vertices?

Mathematics
1 answer:
Ierofanga [76]3 years ago
4 0

Answer:

<h3>A cube</h3>

Step-by-step explanation:

Vertices of a solid shape is a point where 2 lines or edges of the shape intersects. If tom has a cube a rectangular prism and a triangular prism, then the cube has 8 vertices, a rectangular prism has 5 vertices (a rectangle has 4 vertices plus the point where all the lines coming from the vertices of the rectangle intersects).

Also, a triangular prism has 4 vertices(a triangle has 3 vertices plus the point where all the lines coming from the vertices of the triangle intersects)

Hence the only shape that has more than 6 vertices is a cube.

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What's the answer to (230-180+10) x 32+3
Volgvan

Answer:

Step-by-step explanation:

1. Solve what is in parenthesis first. (230-180+10) = 60

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Prove: Every point of S=(0, 1) is an interior point of S.
myrzilka [38]

Answer:

Proved

Step-by-step explanation:

To prove that every point in the open interval (0,1) is an interior point of S

This we can prove by contradiction method.

Let, if possible c be a point in the interval which is not an interior point.

Then c has a neighbourhood which contains atleast one point not in (0,1)

Let d be the point which is in neighbourhood of c but not in S(0,1)

Then the points between c and d would be either in (0,1) or not in (0,1)

If out of all points say d1,d2..... we find that dn is a point which is in (0,1) and dn+1 is not in (0,1) however large n is.

Then we find that dn is a boundary point of S

But since S is an open interval there is no boundary point hence we get a contradiction. Our assumption was wrong.

Every point of S=(0, 1) is an interior point of S.

3 0
3 years ago
What is the volume of a small cone if:
Amiraneli [1.4K]

Answer:

Volume of smaller cone =301.44

Step-by-step explanation:

First let angle of cone be\alpha.

then sin(\alpha ) = 3/5       (For bigger triangle)

Same cone angle is for smaller one because they are similar.

cos(\alpha ) = 4/5

Now for smaller cone radius be R

3/5 =R/Slant height

Slant height =5/3R

Lateral surface area =\frac{1}{2}R^{2}\beta  [R = slant height]  

Given lateral surface area =60\pi =\frac{1}{2}(\frac{5R}{3} )^{2} \beta   ...................................1

2\pi R=\frac{5R}{3}\beta        ................................................2

\beta=\frac{6\pi }{5}

Put angle beta in equation 1 and find the value of R

R =6 cm

Height =\frac{4R}{3}

Thus volume =\frac{1}{3}\pi6^{2}*8

                     =301.44

4 0
3 years ago
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