I 5) From a sector of a circle subtending an angle of 135º and radius 14cm, a cup in form of a cone is made

Use it
Determine:

a) the radius of the conical cup.
(3 marks)

b) the volume of the cup

a. 5.25cm

b. 374.6 cm^2

Step-by-step explanation:

The radius of the conical cup is half the length of the arc formed

Mathematically, the length of the arc would be;

L = theta/360 * 2 * pi * r

L = 135/360 * 2 * 22/7 * 14 = 33 cm

Now, the arc of this sector will become the base circumference of the circular base of the cone

Thus;

2 * pi * R = 33

2 * 22/7 * R = 33

R = (7 * 33)/44 = 5.25 cm

b. The volume of the cone

Kindly note that the radius of the circle becomes the height of the cone

Mathematically;

V = 1/3 * pi * r^2 * h

Kindly note that the radius of the circle will become the slang height of the cone

We can use pythagoras’ theorem to find the height of the cone

Pythagoras theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

So here, slant height l is the hypotenuse, h and r are the other two sides

So 14^2 -5.25^2 = h^2

h^2 = 168.4375

h = 12.98 cm

Volume is thus ;

1/3 * pi * 5.25^2 * 12.98 = 374.6 cm^3

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step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752