Volume Formulas Quiz for Grade 10

Answer explanation

To solve for h, rearrange the volume formula V = πr²h. Divide both sides by πr² to isolate h: h = V/(πr²). Thus, the correct answer is h = \frac{V}{\pi r^2}.

Answer explanation

To solve for r, start with V = πr²h. Rearranging gives r² = V/(πh). Taking the square root results in r = √(V/(πh)), which matches the correct answer: r = √(V/(πh)).

Answer explanation

To solve for B, start with the volume formula V = (1/3)Bh. Multiply both sides by 3 to get 3V = Bh. Then, divide both sides by h to isolate B: B = 3V/h. Thus, the correct answer is B = \frac{3V}{h}.

Answer explanation

To solve for h, start with V = (1/3)πr²h. Multiply both sides by 3 to get 3V = πr²h. Then, divide by πr² to isolate h: h = 3V/(πr²). Thus, the correct answer is h = \frac{3V}{\pi r^2}.

Answer explanation

To solve for r, start with V = (1/3)πr²h. Multiply both sides by 3 to get 3V = πr²h. Then, divide by πh: r² = (3V)/(πh). Finally, take the square root: r = √(3V/(πh)), which matches the correct choice.

Answer explanation

To solve for h, start with V = (1/3)Bh. Multiply both sides by 3 to get 3V = Bh. Then, divide both sides by B to isolate h: h = 3V/B. Thus, the correct answer is h = \frac{3V}{B}.

Answer explanation

To find the side length of a square from its area, we use the formula A = s². Rearranging gives s = √A, making this the correct equation. The other options do not correctly relate the area to the side length.

• b = 2A/h

• b = A/2h

• b = h/2A

• b = 2h/A

Answer explanation

To solve for b in the equation A=\frac{1}{2}bh, multiply both sides by 2 to get 2A=bh. Then, divide both sides by h to isolate b, resulting in b=\frac{2A}{h}. Thus, the correct answer is b=2A/h.

Answer explanation

To solve for V in the equation L=\frac{V}{WH}, multiply both sides by WH. This gives V = L \cdot WH, confirming that the correct answer is V=LWH.

Answer explanation

To solve for r, start with A = πr². Divide both sides by π: r² = A/π. Then, take the square root of both sides to get r = √(A/π). Thus, the correct answer is r = √(A/π).