A sphere of radius 7 in. Is placed inside a rectangular prism with length 15 in., width 18 in., and height 20 in. What is the volume of the prism not occupied by the sphere?

3964 in³

Step-by-step explanation:

volume of sphere:  V = 4/3 πr³

v₁ = 4/3 x 3.14 x 7³ = 1436

volume of prism: v = Bh     B = 15 x 18 = 270    h = 20

v₂ = 270 x 20 = 5400

v₂ - v₁ = 5400 - 1436 = 3964 in³

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,