laneahrose13
Answered

two similar solids a and b are shown

solid a has a volume of 60cm^3
a)find the volume of solid b

solid b has a total surface area of 140cm^2
b)find the total surface area of solid a

two similar solids a and b are shown solid a has a volume of 60cm^3 a)find the volume of solid b solid b has a total surface area of 140cm^2 b)find the total su class=

Answer :

Answer:

see explanation

Step-by-step explanation:

Given 2 similar solids with ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of volumes = a³ : b³

Here ratio of sides = 3 : 6 = 1 : 2 , thus

ratio of areas = 1² : 2² = 1 : 4

ratio of volumes = 1³ : 2³ = 1 : 8

(a)

The volume of solid B is 8 times volume of A, that is

volume of solid B = 8 × 60 = 480 cm³

(b)

The area of solid A is one- quarter the area of solid B, that is

surface area of solid A = 140 ÷ 4 = 35 cm²

akposevictor

Given the two similar solids as shown in the diagram:

a. Volume of Solid B = [tex]\mathbf{480 $ cm^3}[/tex]

b. Surface Area of Solid A = [tex]\mathbf{35 $ cm^2}[/tex]

Given that the two solids, A and B, are similar, therefore, assuming they have a pair of corresponding dimension, given as, a and b respectively, thus:

  • [tex]\mathbf{\frac{Vol_A}{Vol_B} = \frac{a^3}{b^3}}[/tex] (ratio of their volume to their corresponding sides)
  • [tex]\mathbf{\frac{A_A}{A_B} = \frac{a^2}{b^2}}[/tex] (ratio of their surface area to their corresponding sides)

Thus:

a. Volume of Solid A = [tex]60 $ cm^3[/tex]

a = 3 cm

b = 6 cm

  • Substitute

[tex]\frac{60}{Vol_B} = \frac{3^3}{6^3}\\\\\frac{60}{Vol_B} = \frac{27}{216}\\\\Vol_B = \frac{216 \times 60}{27} \\\\\mathbf{Vol_B = 480 $ cm^3}[/tex]

a. Area of Solid B = [tex]140 $ cm^2[/tex]

a = 3 cm

b = 6 cm

  • Substitute

[tex]\frac{A_A}{140} = \frac{3^2}{6^2}\\\\\frac{A_A}{140} = \frac{9}{36}\\\\A_A = \frac{9 \times 140}{36} \\\\\mathbf{A_A = 35 $ cm^2}[/tex]

  • Therefore, given the two similar solids as shown in the diagram:

a. Volume of Solid B = [tex]\mathbf{480 $ cm^3}[/tex]

b. Surface Area of Solid A = [tex]\mathbf{35 $ cm^2}[/tex]

Learn more here:

https://brainly.com/question/12665986

Other Questions