Question

The radius and height of a cone are in the ratio 3:4 if its volume is 301.44 cm² what is the radius and height

Answer 1

hey there,

r : h = 3 : 4
r = (3/4)h

V = 1/3 (pi) (r^2) (h)
301.44 = 1/3 (pi) (r^2) (h)
(h)(r^2) = 287.854
Substitute r = 3/4 h into the equation
(h)[(3/4 h)^2] = 287.854
h(9/16 h^2) = 287.854
9/16 h^3 = 287.854
h^3 = 511.740
h = 7.99
h = 8

r = 3/4 h
r = 3/4 (8)
r = 6

Slant height = sqrt[h^2 + r^2]
s = sqrt[8^2 + 6^2]
s = sqrt[64 + 36]
s = sqrt(100)
s = 10

Radius = 6 cm
Slant height = 10 cm 

Hope this helps!

Answer 2

AnswEr:

Let the radius r and height h of the cone be 3x cm and 4x cm respectively.

Then,

$\mathfrak\red{Volume=301.44\:cm^3}$

$\rightarrow \tt \frac{1}{3} \pi {r}^{2}h = 301.44 \: {cm}^{3} \\ \\ \rightarrow \tt \frac{1}{3} \times 3.14 \times 3x \times 3x \times 4x = 301.44 \\ \\ \rightarrow \tt \: {x}^{3} = \frac{301.44}{3 \times 4 \times 3.14} \\ \\ \rightarrow \tt {x}^{3} = \frac{301.44}{37.68} = 8 \implies \: x = 2$

_____________________________

$\therefore \mathfrak r = \sf \: radius = 3x = 6cm \\ \mathfrak h = \sf \: height = 4x = 8cm$

$\mathfrak\purple{Now,}$

$\sf \: slant \: height = \tt \sqrt{ {r}^{2} + {h}^{2} } cm \\ \\ = \tt \sqrt{36 + 64} cm \\ \\ \sf= 10 \: cm$

#BAL

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