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trapecia [35]
3 years ago
14

Two similar cones have matching heights and radii whose lengths are in the ratio 7:1 Find the ratio of their surface areas.

Mathematics
1 answer:
goldenfox [79]3 years ago
5 0

Answer:

surface area ratio = 49/1 = 49

Step-by-step explanation:

Two solid figure are similar when they have the same shape and the ratio of their corresponding sides are proportional.

Therefore the ratio of their surface area is the side ratio squared.

For a similar shape the ratio of their surface area is the squared of the scaled factor.

The ratio can be represented as a/b, therefore the surface area ratio can then be represented as (a/b)². Therefore,

7:1 or 7/1

The surface area ratio = (7/1)²

surface area ratio = 49/1 = 49

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Help meez 40 pts use surface area formula of cylinder that is for Lateral surface area and for total surface area
jeka94

Answer:So the radius of the cylinder is 2.65 cm.

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1.  The two circles that make up the caps of the cylinder.

2.  The side of the cylinder, which when "unrolled" is a rectangle.

The area of each end cap can be found from the radius r of the circle, which is given by:

A = πr2

Thus the total area of the caps is 2πr2.

The area of a rectangle is given by:

A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:

P = 2πr

Thus the rectangle's area is rewritten as:

A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr2 + 2πrh

where:

π  is Pi, approximately 3.142

r  is the radius of the cylinder

h  height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.

Example 1: Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Solution:

SA = 2 × π × r2 + 2 × π × r × h

SA = 2 × 3.14 × 42 +  2 × 3.14 × 4 × 3

SA = 6.28 × 16 + 6.28 × 12

SA = 100.48 + 75.36

SA = 175.84

Surface area = 175.84 cm2

Example 2: Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Solution:

The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

TSA = 2πr(r+h)

TSA = 11π (5.5+10)

TSA = 170.5 π

TSA = 535.6 cm2

Example 3: Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution:

Again as in the previous example:

TSA = 2πr(r+h)

TSA = 2π× 17(17+3)

TSA = 2π×17×20

TSA = 2136.56 cm2

Example 4: Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Solution:

The radius of cylinder: r = 6 cm

The height of cylinder: h = 9 cm

Total surface area of cylinder is therefore:

TSA = 2πr(r + h)

TSA = 12π (6+9)

TSA = 180 π

TSA = 565.56 cm2

Example 5: Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.

Solution:

Lateral surface area of cylinder is given by:

LSA = 2πrh

Given that:

LSA = 150cm2

h = 9cm

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

LSA = 2πrh

150 = 2× π × r × 9

r = 150 / (2×9× π)

r = 2.65cm

So the radius of the cylinder is 2.65 cm.

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2 years ago
PLEASE HELP!!
lys-0071 [83]
The lines that intersect is B
4 0
3 years ago
I need help please in ese
Alisiya [41]

Answer:

Step-by-step explanation:

In where my friend

Mark me as brainliest

5 0
3 years ago
PLSSS HELP IF YOU TURLY KNOW THISS
algol [13]
I think it is 0.149x10^-4
6 0
2 years ago
What is a name for the marked angle?<br> A: CAD<br> B: CDA<br> C: FAB<br> D: FDA
cluponka [151]

Answer:

A.) Angle CAD

Step-by-step explanation:

Hope this helps! :)

3 0
3 years ago
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