Question

Can you help me with these 5 questions?

Answer 1

1.

Use the formula for the surface area of a sphere:

$\sf A=4\pi r^2$

Plug in what we know:

$\sf A=4\pi (7)^2$

Simplify the exponent:

$\sf A=4\pi (49)$

Multiply:

$\sf A=196\pi~cm^2$

This is an exact answer, if you want an approximate answer you can input 3.14 for pi:

$\sf A\approx 196(3.14)\approx 615.44~cm^2$

2.

Use the formula for the volume of a sphere:

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

Plug in what we know:

$\sf V=\dfrac{4}{3}\pi (11)^3$

Simplify the exponent:

$\sf V=\dfrac{4}{3}\pi (1331)$

Multiply:

$\sf V=\dfrac{5324}{3}\pi~ft^3$ 

This is an exact answer, if you want an approximate answer you can plug in 3.14 for pi:

$\sf V\approx\dfrac{5324}{3}(3.14)\approx 5572.45~ft^3$

3.

Since the two figures are similar, the ratio of their sides must be equal. So we can set up a proportion:

$\sf\dfrac{9}{6}=\dfrac{13.5}{x}$

Cross multiply:

$\sf (6)(13.5)=(9)(x)$

$\sf 81=9x$

Divide 9 to both sides:

$\sf x=\boxed{\sf 9~mm}$