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4 years ago

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The radius of a large sphere is 8 times the radius of a small sphere. the surface area of the large sphere is how many times the

surface area of the small sphere?

1 answer:

kondaur [170]4 years ago

8 0

Large sphere's radius = R,
small sphere's radius = r, R = 8r
surface area of a sphere (SA) = 4×pi×radius^2
So what we need is the SA of the larger in terms of the smaller sphere, so if:
SA (of R) = 4×pi×R^2, then plug in "8r" for "R"...
SA = 4×pi×(8r)^2 = 4×3.14×64r^2
SA = 12.57×64r^2 = 804 r^2
Therefore the SA of the larger sphere is 804 times the SA of the smaller sphere.
I hope that makes sense!

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Answer:

Step-by-step explanation:

(A) The radius of the circle is=1.8m

Then diameter will be: 2r= $2{\times}1.8=3.6 m$

Circumference of circle= ${\pi}d$ = $3.14{\times}3.6=11.304 m$

Area of the circle= ${\pi}r^{2}=3.14{\times}(1.8)^{2}=10.17 m^{2}$

(B) The area of the rectangular backboard of basketball court = 18900 $cm^{2}$

Width=180cm

Area of rectangle= l{\times}b[/tex]

18900=l{\times}180[/tex]

$l=105 cm=1.05m$

Perimeter of the seating space=2(l+b)

= $2(32.5+18.4)$

= $101.8 m$

Perimeter of the basketball court=2(l+b)

= $2(15+28)$

= $86 m$

Now, total perimeter= perimeter of the basketball court+perimeter of the seating space.

Total perimeter= $101.8+86=187.8 m$

Area of the seating space= $l{\times}b$

= $32.5{\times}18.4=598 m^{2}$

(C) The shape consists of one square and 4 triangles, therefore area of square= $(side)^{2}=(3)^{2}=9 m^{2}$

Area of 4 triangles= $4{\times}(\frac{1}{2}{\times}B{\times}H)$

= $4{\times}(\frac{1}{2}{\times}3{\times}2)=12m^{2}$

Area of the shape= Area of the square+ area of the 4 triangles

= $9+12=21m^{2}$

(D) Perimeter of rectangle with length=40 m (After converting cm to m) and breadth= 10 m is given by: $2(l+b)=2(40+10)=100 m$

Perimeter of rectangle with length 68 m and breadth=33 m is given by: $2(l+b)=2(68+33)=202 m$

Perimeter of the semicircle= $\frac{{\pi}d}{2}=\frac{3.14{\times}34}{2}=53.38 m$

Total perimeter= $100+201+53.38=355.38 m$

Area of rectangle with length=40 m (After converting cm to m) and breadth= 10 m is given by: $l{\times}b=40{\times}10=400 m^{2}$

Area of rectangle with length 68 m and breadth=33 m is given by: $l{\times}b=68{\times}33=2244 m^{2}$

Area of the semi circle= $\frac{{\pi}r^{2}}{2}=\frac{3.14{\times}17^{2}}{2}=453.73 m^{2}$

Total area= $400+2244+453.73=3097.73 m^{2}$

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3 years ago

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3 years ago

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3 years ago

The sum of eight and a number is one hundred. What is the number

vaieri [72.5K]

Let the number be x.

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8 + x = 100

x = 100 - 8

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4 years ago

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IgorLugansk [536]

The solution to the system of equations is (3, 2)

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Give the system of equation below

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y=x-1

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x = 3

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