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oksano4ka [1.4K]
3 years ago
13

4 The ratio of corresponding dimensions of two similar solids is 3/4. The surface

Mathematics
2 answers:
Nookie1986 [14]3 years ago
8 0
Question 4:

---------------------------------------------------
Ratio of Dimension to Area
----------------------------------------------------
Dimension : Area
\frac{3}{4}  \  : \  (\frac{3}{4} )^2
\frac{3}{4} \ :  \frac{9}{16}

---------------------------------------------------
Find Area
----------------------------------------------------
Let x be the surface area of the second solid
\frac{9}{16}  =  \frac{96}{x}
9x = 96 \times 16
9x = 1536
x = 1536 \div 9
x =170.7 m^2 (\ nearest \ tenth )

---------------------------------------------------
Answer: 170.7 m²
----------------------------------------------------


---------------------------------------------------
Ratio of Dimension to Volume
----------------------------------------------------
Dimension : Volume
\frac{3}{4} \ : \ (\frac{3}{4} )^3
\frac{3}{4} \ : \ \frac{27}{64}

---------------------------------------------------
Find Volume
----------------------------------------------------
Let x be the surface are of the second solid
\frac{27}{64} = \frac{720}{x}
27x = 720 \times 64
9x = 46080
x = 146080 \div 27
x =1706.7 m^2 (nearest \ hundredth )

---------------------------------------------------
Answer: 1706.7 m³
----------------------------------------------------


Question 5
---------------------------------------------------
Find Radius
---------------------------------------------------
Radius = Diameter ÷ 2
Radius = 40 ÷ 2
Radius = 20

---------------------------------------------------
Find volume of the globe, which is a sphere
---------------------------------------------------
Volume \ of \ sphere \ =  \frac{4}{3}  \pi  x^{3}

Volume \ of \ sphere \ = \frac{4}{3} \pi (20)^{3}

Volume \ of \ sphere \ = 33510.3 in^3 \ ( \ nearest \ hundredth )

---------------------------------------------------
Answer: 33510.3 in³
----------------------------------------------------

White raven [17]3 years ago
6 0
4.

The ratio is 3/4 for corresponding dimensions, the ratio of their surface areas is equal to the square of this ratio:

\sf (\dfrac{3}{4})^2=\dfrac{S}{96}

Simplify the exponent:

\sf \dfrac{9}{16}=\dfrac{96}{S}

Cross multiply:

\sf 9S=1536

Divide 9 to both sides:

\sf S\approx 170.7~m^2

So the surface area of the second solid is 54 square meters.

The ratio is 3/4 for corresponding dimensions, the ratio of their volumes is equal to the cube of this ratio:

\sf (\dfrac{3}{4})^3=\dfrac{720}{V}

Simplify the exponent:

\sf \dfrac{27}{64}=\dfrac{720}{V}

Cross multiply:

\sf 27V=46080

Divide 64 to both sides:

\sf V\approx 1706.7~m^3

5.

A globe is a sphere, use the formula for the volume of a sphere:

\sf V=\dfrac{4}{3}\pi r^3

The radius is half of the diameter, so the radius here is 40/2 = 20. Plug it in the formula, use 3.14 to approximate for Pi:

\sf V=\dfrac{4}{3}(3.14)(20)^3

Simplify the exponent:

\sf V=\dfrac{4}{3}(3.14)(8000)

Multiply:

\sf V\approx \boxed{\sf 33,493~in^3}
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