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3 years ago

a cone has a radius of 6cm and height 9 calculate a)the volume and curved surface area b) total surface area

Mathematics

1 answer:

Orlov [11]3 years ago

3 0

Answer:

V = 339.3 cm³; L = 203.9 cm²; A = 317.0 cm²

Step-by-step explanation:

a) Volume

The formula for the volume (V) of a cone is

V = ⅓πr²h

V = ⅓π × 6² × 9

V = ⅓π × 36 × 9

V = 108π cm³

V ≈ 339.3 cm³

=====

Curved surface area

The formula for the lateral surface area (L) of a cone is

L = πr√(r² + h²)

L = π×6√(36 + 81)

L = 6π√[9(4 + 9)]

L = 6π√(9 × 13)

L = 18π√13 cm²

L ≈ 203.9 cm²

===============

b) Base surface area

The base is a circle, so the formula for base surface area (B) is

B = πr²

B = π×6²

B = 36π cm²

B ≈ 113.1 cm²

=====

Total surface area

A = L + B

A = 18π√(13 +36π)

A = 18π(2 + √13) cm²

A ≈ 203.9 + 113.1

A ≈ 317.0 cm²

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netineya [11]

Answer:

d. 42 degrees

Step-by-step explanation:

y and 92 are supplemetary angles, which means they both add up to 180 since they are on the straight line.

Hence,

y+92 = 180

y = 180-92

y=88

And now we also know that all the angles of a traingle add up to 180,

so, we can simply find the x by:

88+x+50 =180

138 + x =180

x = 180-138

x = 42

Hope this helps!

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5 0

3 years ago

What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]? A. maximum point: (–2.4, 3

slava [35]

Answer:

(-2.4, 37.014)

Step-by-step explanation:

We are not told how to approach this problem.

One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually. A good graph done on a graphing calculator would be sufficient info for this estimation. My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.

Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3]. In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.

Optional: Another approach would be to use calculus: we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x. There would be four x-values, which we'd call "critical values."

3 0

3 years ago

Read 2 more answers

A ball has been thrown into the air its distance from the ground is given by the function s(t)=-16t^2+96t+100

slega [8]

Answer:

For t=3 sec the velocity change from positive to negative

Step-by-step explanation:

we have

$s(t)=-16t^2+96t+100$