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lilavasa [31]
3 years ago
6

A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and

the lateral area of the cylinder.
Mathematics
1 answer:
Papessa [141]3 years ago
5 0

Answer:

1 : 1

Step-by-step explanation:

When a circle is inscribed in a cylinder, the height of the cylinder is equal to the diameter of the sphere and the radius of the cylinder is same as that of the sphere.

Let the radius of sphere is r.

height of cylinder, h = 2r

radius of cylinder = r

Surface area of sphere, A = 4πr²

lateral surface area of cylinder, A' = 2 πrh

A' = 2πr x 2r = 4πr²

The ratio of surface area of sphere to the lateral surface area of cylinder is 1 : 1.

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Step-by-step explanation:

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Plot the following points to create a rectangle.
Tanya [424]

Answer:

(5, -1)

Step-by-step explanation:

The three coordinates of a triangle are given as:

(5,3), (-5,3), (-5,-1).

To find:

The missing vertex = ?

Solution:

Let us label the vertices:

A (5,3),

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C(-5,-1).

Let the missing vertex be (x, y).

Let us recall the properties of a rectangle.

The <em>opposite sides</em> of the rectangle are equal and parallel to each other.

Let us consider the side AB, we can see that only x coordinate is changed from A to B.

Let us consider the side BC, we can see that only y coordinate is changed from B to C.

A and B are adjacent vertices.

Similarly the opposite vertices will be C and D.

Same pattern will be followed in CD as that of AB.

x coordinate will be changed by same difference as that of AB.

Change in x coordinate from D to C = -5-x

Change in x coordinate from A to B = -5-5 =-10

Equating them:

-5-x=-10\\\Rightarrow x = 5

Same pattern is followed in BC and AD.

Their change in y coordinate will be same.

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Missing vertex is <em>(5, -1)</em>.

Please refer to the attached image for the rectangle.

3 0
3 years ago
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