Question

The area of the largest cross section of a sphere and the circumference of the sphere are in the ratio 4:1.

Answer 1

Answer:

$(a)\ r = 8cm$

$(b\ Area = 200.96cm^2$

$(c)\ Volume = 2143.573cm^3$

Step-by-step explanation:

The largest cross-section of a sphere is the center.

So, we have:

$A : C = 4 : 1$

Where

$A = \pi r^2$

$C =2\pi r$

Solving (a): The radius

$A : C = 4 : 1$ implies that

$\pi r^2 : 2\pi r = 4 : 1$

Express as fraction

$\frac{\pi r^2 }{ 2\pi r} = \frac{4 }{ 1}$

$\frac{\pi r^2 }{ 2\pi r} = 4$

Divide by $\pi r$

$\frac{r}{ 2} = 4$

Make r the subject

$r = 4 * 2$

$r = 8cm$

Solving (b): Area of the largest cross-section.

$Area = \pi r^2$

$Area = 3.14 *8^2$

$Area = 200.96cm^2$

Solving (b): Volume of the sphere

$Volume =\frac{4}{3}\pi r^3$

$Volume =\frac{4}{3} * 3.14 * 8^3$

$Volume = 2143.573cm^3$