Question

GIVING MEDALS!!!!!!


Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Answer 1

erm... are there options?

Answer 2

No, but i got 28027.76 ?

Answer 3

I don't know how to do this sorry :(
@sourwing @jdoe0001 @MathLegend help?

Answer 4

do you know what a square pyramid looks like?

Answer 5

I couldn't tell if height meant slant height or other

Answer 6

Height is from the point of the triangle to the middle of the square on the bottom. Slant height is one of the 4 lines connecting to the top to a corner on the square.

Answer 7

you're asked to find the "surface area"
notice the pyramid has 4 triangular faces
and 1 squarish bottom

the surface area is, the SUM of all those areas

the bottom is simple, is a square, and you're given the dimensions

the triangular faces, you're given the "base" of the triangle

but notice the picture, you can just use pythagorean theorem to get the "slant height" of the pyramid, which is really the "height" of the triangular face

once you have the "height" of the triangular face, recall that area of a triangle = \(\bf \frac{1}{2}\cdot base\cdot height\)

Answer 8

so 4 triangles
slant height = sqrt ( 75^2 + 50^2 )
triangle = (1/2) (slant height) (base length)
= (1/2) (sqrt ( 75^2 + 50^2 )) (100)
base square = (100) (100)

so surface area = (4*(1/2)*(sqrt(8125))*(100)) + 1000 = ?

Answer 9

kinda forgot to put the 50 in the picture... but anyhow, just use the pythagorean theorem to find the slant height :)

Answer 10

@jigglypuff314 do you understand?

Answer 11

they've pointed in the right direction :)
"surface area = (4*(1/2)*(sqrt(8125))*(100)) + 1000 = ? "

Answer 12

19027.76

Answer 13

yes :) that's what I got at least :P

Answer 14

What about this one? Find the volume of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Answer 15

\(\bf \textit{volume of a pyramid}=\cfrac{1}{3}\cdot \textit{area of base}\cdot height
\)

Answer 16

as in
area of base = (100)(100)

so volume = (1/3) (100)(100) (75) = ?

Answer 17

250,000 ?

Answer 18

yeah :)

Answer 19

oh crap, which made me just realize that there was a typo in the other one, sorry
surface area = (4*(1/2)*(sqrt(8125))*(100)) + 10000 = ?
^missed a zero

Answer 20

28027.76 :) And if you look further in the convo... I said that earlier lol

Answer 21

lol XD >,< Ima just a bit cross eyed :P

Answer 22

Find the radius of the base of a cone with volume equal to 144π in3 and height equal to 12 in

Answer 23

volume = (1/3) (area of base) (height)
area of base = pi r^2

volume = (1/3) (pi r^2) (height)

144pi = (1/3) (pi r^2) (12) solve for r

Answer 24

What is it? I can't seem to find an answer.. ;o

Answer 25

(12/3) pi r^2 = 144pi divide both sides by 4pi

r^2 = 36 sqrt both sides

r = sqrt 36 = ?

Answer 26

6

Answer 27

Last one :) What is the volume of a pyramid that has a base with an area of 81 square feet and a height of 4 feet?

Answer 28

108 right?

Answer 29

volume of pyramid = (1/3) (area of base) (height)
= (1/3) (81) (4)

108 is correct :)

Answer 30

kk :) ty! Night! :D