Question

which of these shapes has a volume of greater than 300 cubic centimeters?
a. cylinder (radius = 3cm, height = 10cm) - use π≈3.14
b. cube (side = 5cm)
c. rectangular prism (length = 10cm, width = 10cm, height = 3cm)
d. triangular prism (base = 4 cm, height of base = 3 cm, length = 10cm)

Explanation:

Step1: Calculate cylinder volume

Volume formula for cylinder \(V=\pi r^{2}h\). Substitute \(r = 3\), \(h=10\), \(\pi\approx3.14\).
\(V=3.14\times3^{2}\times10=3.14\times9\times 10 = 282.6\ \text{cm}^3\)

Step2: Calculate cube volume

Volume formula for cube \(V = s^{3}\). Substitute \(s = 5\).
\(V=5^{3}=125\ \text{cm}^3\)

Step3: Calculate rectangular prism volume

Volume formula for rectangular prism \(V=l\times w\times h\). Substitute \(l = 10\), \(w = 10\), \(h = 3\).
\(V=10\times10\times3=300\ \text{cm}^3\)

Step4: Calculate triangular prism volume

Volume formula for triangular prism \(V=\frac{1}{2}\times b\times h_{base}\times l\). Substitute \(b = 4\), \(h_{base}=3\), \(l = 10\).
\(V=\frac{1}{2}\times4\times3\times10=60\ \text{cm}^3\)

Answer:

None of the options (a: \(282.6\ \text{cm}^3<300\ \text{cm}^3\), b: \(125\ \text{cm}^3<300\ \text{cm}^3\), c: \(300\ \text{cm}^3 = 300\ \text{cm}^3\) (not greater), d: \(60\ \text{cm}^3<300\ \text{cm}^3\)) have a volume greater than \(300\) cubic centimeters. If there is a mistake in problem - reading (e.g., if in option c, height is misread), but based on given data, no correct answer. If we assume a strict interpretation of "greater than" (exclusive), no option satisfies. If inclusive (but the problem says "greater than"), still no. But if we check calculations again:

• Cylinder: \(V=\pi r^{2}h=3.14\times9\times10 = 282.6\)
• Cube: \(V = 125\)
• Rectangular prism: \(V=300\) (not greater)
• Triangular prism: \(V = 60\)