Question

The radius of the base and height of a right circular cone are in the ratio 8 : 15. Find the slant height of the cone if its volume is 1005 5/7 cm³.

• A. 15 cm
• B. 17 cm
• C. 8 cm
• D. 23 cm

Answer 1

Answer:

B. 17 cm

Given ratio:

$r : h = 8 : 15$
$\Rightarrow r = 8k,; h = 15k$

Use volume of cone

$V = \frac{1}{3}\pi r^2 h$
$1005 \tfrac{5}{7} = \frac{1}{3}\times \frac{22}{7} \times (8k)^2 \times (15k)$
Convert mixed fraction:
$1005 \tfrac{5}{7} = \frac{7040}{7}$
Substitute

$\frac{7040}{7} = \frac{1}{3}\times \frac{22}{7} \times 64k^2 \times 15k$
$= \frac{22 \times 64 \times 15}{3 \times 7} k^3$
$= \frac{22 \times 64 \times 5}{7} k^3$
$= \frac{7040}{7} k^3$
Compare

$\frac{7040}{7} = \frac{7040}{7} k^3$
$\Rightarrow k^3 = 1 \Rightarrow k = 1$

So:
$r = 8,\quad h = 15$
Slant height

$l = \sqrt{r^2 + h^2}$
$l = \sqrt{r^2 + h^2}$

$l = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$

$\boxed{17 \text{ cm}}$