Consider the volumes of the following 1. A parallelopiped of length 5 cm, breadth 3 cm and height 4 cm 2. A cube of each side 4 cm 3. A cylinder of radius 3 cm and length 3 cm 4. A sphere of radius 3 cm The volumes of these in the decreasing order is :

### Concept & Volume Calculations Evaluate the volume of each fundamental 3D shape independently using their respective formulas, and then sort the numerical results. $$ V_{\text{cuboid}} = l \times b \times h $$ $$ V_{\text{cube}} = a^3 $$ $$ V_{\text{cylinder}} = \pi r^2 h $$ $$ V_{\text{sphere}} = \frac{4}{3} \pi r^3 $$ ### Step-by-Step Solution - **1. Parallelopiped (Cuboid):** $l = 5$, $b = 3$, $h = 4$. $V_1 = 5 \times 3 \times 4 = 60$ cm$^3$. - **2. Cube:** side $a = 4$. $V_2 = 4^3 = 4 \times 4 \times 4 = 64$ cm$^3$. - **3. Cylinder:** radius $r = 3$, length (height) $h = 3$. Use $\pi \approx 3.14$. $V_3 = \pi \times 3^2 \times 3 = 27\pi \approx 27 \times 3.1415 = 84.82$ cm$^3$. - **4. Sphere:** radius $r = 3$. $V_4 = \frac{4}{3} \pi \times 3^3 = \frac{4}{3} \pi \times 27 = 36\pi \approx 36 \times 3.1415 = 113.09$ cm$^3$. - Comparing the values: $V_4 (113) > V_3 (84.8) > V_2 (64) > V_1 (60)$. - The decreasing order is 4, 3, 2, 1. ### Exam Strategy & Shortcut To quickly approximate without deep decimals, use $\pi > 3$. For cylinder: $27 \times 3 = 81$ (so it's $> 81$). For sphere: $36 \times 3 = 108$ (so it's $> 108$). This immediately establishes that $36\pi > 27\pi > 64 > 60$, giving the correct sequence instantly. ### Common Pitfall Using the diameter instead of the radius for the sphere or cylinder, or incorrectly calculating $4^3$ as $16$ instead of $64$. ### Final Answer Therefore, the correct answer is **4, 3, 2, 1**.