Question

50 Points to the person who helps me and Brainliest

Answer 1

Answer:

$h\approx9.54\text{ cm}$

Step-by-step explanation:

First, we know that the slant height is 10 cm and the diameter is 6 cm.

Since our diameter is 6 cm, our radius is just half of that. Namely:

$r=\frac{1}{2}(6)=3$

To find the vertical height, we can use some geometry.

If we look closely, we can see that the vertical height, slant height, and the radius form a right triangle.

So, to find the vertical height, we can use the Pythagorean Theorem:

$a^2+b^2=c^2$

In this case, c, our hypotenuse, is our slant height.

So, let's substitute 3 for a, h for b, and 10 for c. This yields:

$3^2+h^2=10^2$

Square:

$9+h^2=100$

Subtract 9 from both sides:

$h^2=91$

Take the square root of both sides:

$h=\sqrt{91}$

Approximate. Use a calculator. So:

$h\approx9.54\text{ cm}$

And we're done!

Edit: Added Unit

Answer 2

Answer:

9.69 or 9.70

Step-by-step explanation:

Equation: π•r^2•h/3

Diameter (d): 6

Radius (r): 6/2 (d/2)

r: 3

π•3^2•h/3

Now, we use the Pythagorean Theorem to solve for h:

Equation: a^2+b^2=c^2

Hypotenuse (c): 10

Radius (r): 3

a^2+3^2=10^2

a^2+9=100

a^2+9-9=100-9

a^2=91

√a^2=√91

a≈9.5393...

Height: 9.54

π•3^2•9.54/3≈89.91