# How to add pi and math questions?

Im confused about something... my teacher was doing a formula for surface area he had something like 36 pi + 64 pi and together its 100 pi... should it not be pi squared or something?

I tried something similar right now, i had two sets of 2 pi that i divided by a number, and got one answer, when i combined them to make 4 pi i got a different answer...

BONUS IF ANYONE CAN EXPLAIN THESE PROBLEMS OR ANY ONE OF THEM:

A cone has a surface area of 100mm squared The height is twice the radius. What is the height of the cone?

A rectangular prism which a length and width of 10cm and a height of 20cm is half full of juice. A round ball with a diameter of 4cm is dropped into this rectangular prism. How far will the water level rise once the sphere is completely underwater?

A ball has a diameter of 10cm estimate the height of the smallest box in which the ball will fit in in inches

### 4 Answers

- BrainardLv 75 years agoFavorite Answer
36 pi + 64 pi = ( 36 + 64) * pi

= (100) *pi

= 100pi

Let r = radius, then h = 2r

Surface area of a cone is given by

S = pi*r *l + pi * r^2, ...........(1) where l is the slant height

Now l^2 = r^2 + (2r)^2

= r^2 + 4r^2

= 5r^2

l = r * sqrt(5)

Now put this in equation (1)

S = pi * r * r sqrt(5) + pi*r^2

= pi*r^2sqrt(5) + pi*r^2

= r^2 ( pisqrt(5) + pi)

Therefore

r^2 ( pisqrt(5) + pi) = 100

r^2 = 100/[pisqrt(5) + pi]

r = sqrt[ 100/[pisqrt(5) + pi] ]

h = 2 sqrt[ 100/[pisqrt(5) + pi] ]

= 2 sqrt(9.836)

= 2* 3.136290234

= 6.272580468

= 6 . 3 mm

Let h = rise

Then

100h = 4/3 pi r^3

= 4/3 pi (2)^3

= 32/3 pi

= 33.51032164

h = 0. 335 cm

- Hammed SanusiLv 45 years ago
36π + 64π = 100π

(1)

A cone has a surface area of 100mm squared The height is twice the radius. What is the height of the cone?

SOLUTION

Area of a cone = πr[r+√(h²+r²)]

Let the surface area of the cone be,100mm² (Given):

Let the height of the cone be, h

Let the radius of the cone be, r

The height is twice the radius means

h = 2r

Now from the formula:

Area of a cone = πr[r+√(h²+r²)]

Area = 100mm², r = r mm, h = 2r mm

100 = πr[r+√{(2r)²+r²}]

100 = πr[r+√(4r²+r²)]

100 = πr[r+√(5r²)]

Divide both side by πr

100/πr = r + √(5r²)

Take r to the other side. .

(100/πr) - r = √(5r²)

Square both side to get. ..

[√(5r²)]² = [(100/πr) - r]²

5r² = (100/πr - r)(100/πr - r)

Expand the Right hand side to get. .

5r² = (10000/π²r²)-(100r/πr)-(100r/πr)+r²

5r² = (10000/π²r²)-(100/π)-(100/π)+r²

5r² = (10000/π²r²)-2(100/π)+r²

But π = 22/7 (constant). .

π² = (22/7)² = 484/49

5r²=[10000/(484/49)r²]-2[100/(484/49)]+r²

5r²=[490,000/484r²]-2[4,900/484]+r²

5r² = (122500/121r²)-2(1225/121)+r²

Take r² to the other side

5r²-r² = (122500/121r²)-(2450/121)

4r² = (122500/121r²)-(2450/121)

Find the L.C.M on the Right hand side..

4r² = (122500 - 2450r²)/121r²

Cross multiply to get ...

484r⁴ = 122500 - 2450r²

Re arrange to form an equation..

484r⁴ + 2450r² - 122500 = 0

This can be re write as .....

484(r²)² + 2450r² - 122500 = 0

Divide through by 2 to reduce the equation

242(r²)² + 1225r² - 61250 = 0

Using quadratic formula...

a = 242, b = 1225, c = -61250

r² = [-b ± √(b² - 4ac)]/2a

r² = [-1225±√(1225)²-4(242)(-61250)]/(2×242)

r² = [-1225±√(1500625+59290000)]/(484)

r² = [-1225±√(60790625)]/(484)

r² = (-1225 ± 7796.834293)/(484)

r² = (-1225/484)±(7796.834293/484)

r² = -2.5310 ± 16.1092

r² = (-2.5310+16.1092) or (-2.5310-16.1092)

r² = 13.5782 or r² = -18.6402

Since negative is not allowed..

r² = 13.5782

Take the square root of both side

√(r²) = √(13.5782)

∴ r = 3.68486092

∴ r = 3.68

Since, h = 2r

∴ h = 2(3.68)

∴ h = 7.36 mm

Therefore, the height of the cone, h = 7.36 mm

One after the other.

- DWReadLv 75 years ago
You've forgotten the distributive rule!

36π + 64π = (36+64)π = 100π

:::::

r, h, and ℓ are the radius, height, and slant length, respectively.

lateral area = πrℓ

base area = πr²

surface area = πrℓ + πr²

"A cone has a surface area of 100mm squared"

πrℓ + πr² = 100

"The height is twice the radius"

h = 2r

h² + r² = ℓ²

4r² + r² = ℓ²

ℓ = r√5

πr(r√5) + πr² = 100

πr²√5 + πr² = 100

πr²(1+√5) = 100

r² = 100/(π(1+√5))

r = 10/√(π(1+√5))

h = 20/√(π(1+√5))

you can do the calculation