Find the values of θ between 0° and 360° satisfying the equation 5 sin θ = -4.

March 17, 2026Mathematics

ScanSolve AI Answer

March 17, 2026

Answer

$100\pi cm^{3}$

Step 1: Find the height $h$ using the slant height formula.

l^{2} = r^{2} + h^{2}

Substitute $r = 5$ cm and $l = 13$ cm:

13^{2} = 5^{2} + h^{2}

169 = 25 + h^{2}

h^{2} = 169 - 25

h^{2} = 144

h = \sqrt{144}

h = 12 cm

Step 2: Find the volume $V$ of the cone.

V = \frac{1}{3} \pi r^{2} h

Substitute $r = 5$ cm and $h = 12$ cm:

V = \frac{1}{3} \pi (5)^{2} (12)

V = \frac{1}{3} \pi (25) (12)

V = \frac{1}{3} \pi (300)

V = 100 \pi cm^{3}

100\pi \text{ cm^{3}}

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Quick Answer

Find the height h using the slant height formula. l^2 = r^2 + h^2 Substitute r = 5 cm and l = 13 cm: 13^2 = 5^2 + h^2 169 = 25 + h^2 h^2 = 169 - 25 h^2 = 144 h = sqrt(144) h = 12 cm Step 2: Find the volume V of the cone.

Asked on March 17, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 17, 2026

Step 1: Find the height h using the slant height formula. l^2 = r^2 + h^2 Substitute r = 5 cm and l = 13 cm: 13^2 = 5^2 + h^2 169 = 25 + h^2 h^2 = 169 - 25 h^2 = 144 h = sqrt(144) h = 12 cm Step 2: Find the volume V of the cone. V = (1)/(3) r^2 h Substitute r = 5 cm and h = 12 cm: V = (1)/(3) (5)^2 (12) V = (1)/(3) (25) (12) V = (1)/(3) (300) V = 100 cm^3 100 cm^3