Question

Chiquita planned to do the same thing as Rhonda, but she misunderstood what Rhonda meant when she

said "...20% smaller than the one below it." Chiquita made her first ball the same size as Rhonda but

then decreased the volume by 20% for each subsequent ball. How much taller is Chiquita's completed v

snowman than Rhonda's completed snowman? Express your answer as a decimal to the nearest tenth.

Plz show full work

Answer 1

Answer:

to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Step-by-step explanation:

Let Vr1 be the volume of Rhonda’s first ball, and Vc1 be the volume of Chiquita’s first ball. Since the balls are spheres the formula for obtaining their Volume value is given as   V= (4/3) x ∏ r3  

Since from the question we were told that the first snowball for Rhonda and Chiquita’s Snowman are the same.

Let’s assume that the Vr1 =Vc1=10m²  

So to find the radius we make r the subject of formula so r =∛(3V/4∏)  where V is equal to 10 for the first spheres and ∏  is a constant with value 3.142 so  

r1 = ∛(3×10/4)×3.142   = 1.337m

For the Second Snow ball of Rhonda’s Snowman  

Given from the question that first Snow ball is 20% less than the Second Snow Ball

Let Vr2 Denote the volume of the second Rhonda’s Snowball  

Vr2 = 20% of Vr1 + Vr1

       = 20% of 10 + 10

       = (20/100) x 10 + 10

       = 12m²

So to find the radius of the second ball for Rhonda’s Snowman

Let r2 denote the radius of the second ball  

 r2 = ∛(3×12/4)×3.142   = 1.420m

For the Third Snow ball of Rhonda’s Snowman  

Given from the question that Second Snow ball is 20% less than the Third Snow Ball

Let Vr3 denote the volume of the third Rhonda’s Snowball

Vr3 = 20% of Vr2 +Vr2  

             = (20/100) x 12 +12

             = 14.4m²

  So to find radius of the Third ball for Rhonda’s Snowman

Let r3 denote the radius of the second ball  

  r3 =  ∛(3×14.4/4)×3.142   = 1.509m

For the Second Snow ball of Chiquita’s Snowman  

Given from the question that first Snow ball is 20% greater than the Second Snow Ball

Let Vc2 denote the volume of the second Chiquita’s Snowball

For   Vc2 = Vc1 - 20% of Vc1

               = 10 – (20/100) x 10

               = 8m²

So to find the radius of the second ball for Chiquita  

Let c2 denote the radius of the second ball  

c2 =    ∛(3×8/4)×3.142   =1.240m

For the Third Snow ball of Chiquita’s Snowman  

Given from the question that Second Snow ball is 20% greater than the third Snow Ball

Let Vc3 denote the volume of the third Chiquita’s Snowball

For Vc3 = Vc2 - 20% of Vc2

             = 8 – (20/100) x 8

             = 6.4m²

So to find the radius of the second ball for Chiquita  

Let c3 denote the radius of the second ball  

  c3 =∛((3×6.4/4)×3.142)   = 1.151m

Therefore Height of Rhonda’s Snowman = Dr1 + Dr2 + Dr3  

          = 2×r1 +2×r2 +2×r3

          = (2×1.337) + (2×1.420) + (2×1.509)

         = 8.532m

Therefore the Height of Chiquita’s Snowman = Dc1 + Dc2 +Dc3

       = 2×c1 +2×c2 +2×c3

       = (2×1.337) + (2×1.240) + (2×1.151)

      = 7.456m

No to find how much taller Chiquita’s completed snowman is than Rhonda's completed Snowman  

We divide the Height of the Chiquita’s snowman by the height of Rhonda’s Snowman

 i.e. 7.456/8.532 = 0.87

Note: if we assume another value for Vr1 = Vc1 we will still get the same ratio.