If the m∠srw = 85°, what are the measures of ∠vru and ∠urw?
m∠vru = °
m∠urw = °

The measure of m∠VRU and m∠URW are 80 and 15 degrees respectively

From the given diagram;

m∠SRW = m∠TRV

Given the following:

m∠SRW = 85

m∠TRV = 2x + 15

Equating both expressions

2x + 15 = 85

2x = 70

x = 70/2

x = 35

Get m∠VRU

m∠VRU = 2x + 10

m∠VRU = 2(35) + 10

m∠VRU = 80degrees

Get m∠URW:

m∠URW = 180 - (85+80)

m∠URW = 180 - 165

m∠URW = 15degrees

Hence the measure of m∠VRU and m∠URW are 80 and 15 degrees respectively.

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Step-by-step explanation:

∠TRV = ∠SRW ( vertical angles ), hence

2x + 15 = 85 ( subtract 15 from both sides )

2x = 70 ( divide both sides by 2 )

x = 35

Hence

∠VRU = 2x + 10 = ( 2 × 35) + 10 = 70 + 10 = 80°

and

∠URW + ∠VRU + ∠SRW = 180 ( sum of angles in a straight line ), thus

∠URW + 80 + 85 = 180

∠URW + 165 = 180 ( subtract 165 from both sides )

∠URW = 15°

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.