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3 years ago

If the combined area of the white and orange regions is 100π, what is the area of ONLY the orange region?

Mathematics

2 answers:

7nadin3 [17]3 years ago

3 0

64π is correct, since the area of the white circle is 36π, and 100π - 36π = 64π.

Sunny_sXe [5.5K]3 years ago

3 0

The area of orange=total-white

given
all=100pi

remember
area=pi times radius^2
white radius is 6
area=pi6^2
area=36pi

areaorange=areatotal-areawhite
areaorange=100pi-36pi
areaorange=64pi square units

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The volume of pyramid B is 64 times the volume of pyramid A.

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, $s_A =$ 12 inches

Height of A, $h_A =$ 8 inches

Side Length of B, $s_B =$ 48 inches

Height of B, $h_B =$ 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

$V_B$ is how many times bigger than $V_A$ ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

$V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}$

Here, base is square, so:

$V=\dfrac{1}{3} \times s^2 \times h$

Volume of pyramid A:

$V_A=\dfrac{1}{3} \times s_A^2 \times h_A$

$\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3$

Volume of pyramid B:

$V_B=\dfrac{1}{3} \times s_B^2 \times h_B$

$\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3$

The volume of pyramid B is 64 times the volume of pyramid A.

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