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Home » \( A = 5000(1 + 0.06)^3 = 5000(1.06)^3 \) - Nelissen Grade advocaten

\( A = 5000(1 + 0.06)^3 = 5000(1.06)^3 \) - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A cylinder has radius $ r $ and height $ 6r $. A cone has radius $ 2r $ and height $ 3r $. What is the ratio of the volume of the cylinder to the volume of the cone?

📌 Solution: The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 (6r) = 6\pi r^3 $. The volume of the cone is $ V_{\text{cone}} = \frac{1}{3} \pi (2r)^2 (3r) = \frac{1}{3} \pi (4r^2)(3r) = 4\pi r^3 $. The ratio is:

📌 \frac{V_{\text{cyl}}}{V_{\text{cone}}} = \frac{6\pi r^3}{4\pi r^3} = \frac{3}{2}.

📌 Question: A triangle has side lengths of $ 7 \, \text{cm} $, $ 10 \, \text{cm} $, and $ 13 \, \text{cm} $. What is the area of the triangle?

📌 Solution: Use Heron’s formula. The semi-perimeter is:

📌 s = \frac{7 + 10 + 13}{2} = 15 \, \text{cm}.

📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)} = \sqrt{15 \cdot 8 \cdot 5 \cdot 2} = \sqrt{1200} = 10\sqrt{12} = 20\sqrt{3} \, \text{cm}^2.

📌 \boxed{20\sqrt{3}}

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But in decimal form: \( \frac{8}{3} \approx 2.\overline{6} \), so as a...
#### 2.67 (rounded to two decimal places)
A rectangle’s length is 5 meters more than twice its width. If the per...
Let the width be \( w \) meters. Then the length is \( 2w + 5 \) meter...
Perimeter formula:
\[ 2(\text{length} + \text{width}) = 58 \]
\[ 2((2w + 5) + w) = 58 \]
\[ 2(3w + 5) = 58 \]
\[ 6w + 10 = 58 \]
Length = \( 2(8) + 5 = 16 + 5 = 21 \) meters

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