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Leona [35]
3 years ago
13

A cone-shaped popcorn cup has a radius of 5 centimeters and a height of 9 centimeters. How many cubic centimeters of popcorn can

the cup hold?
Use 3.14 for π (pi).
The volume of the popcorn cup is __ cm^3
Mathematics
1 answer:
guajiro [1.7K]3 years ago
5 0

Answer:

The cup can hold 235.5 cubic cm of popcorn.

Step-by-step explanation:

A cone shaped popcorn cup has a radius of 5 cm and a height of 9 cm.

Use 3.14 as an approximation for pi.

Now, to find cubic cm of popcorn the cup can hold.

Radius (r)= 5 cm

Height (h)= 9 cm

\pi= 3.14 (as per question).

So, to get the cubic cm of popcorn the cup can hold we put formula of volume:

Volume= \pirx^{2} h\frac{x}{y} 3

Volume= 3.14 x 5x^{2} × 9\frac{x}{y}3

Volume= 3x14 x 25 x 3

Volume= 235.5 cubic cm.

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Angela tried to solve an equation step by step. \begin{aligned} \dfrac34+m&=\dfrac54\\\\ \dfrac34+m-\dfrac34&=\dfrac54+\
Liono4ka [1.6K]

Answer:

The mistake she made was ; She didn't change the sign when subtracting -3/4 from both sides

She wrote 5/4+3/4 instead of 5/4-3/4

Step-by-step explanation:

Correct solution:

\frac{3}{4}  + m =   \frac{5}{4}

Subtract-3/4 from both sides

\frac{3}{4}  -  \frac{3}{4}  + m =  \frac{5}{4}  -  \frac{3}{4}

Simplify

m =  \frac{5}{4}  -  \frac{3}{4}  \\ m =  \frac{1}{2}

7 0
4 years ago
2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
zlopas [31]
<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

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