Question

1. which of these shapes has a volume of greater than 300 cubic centimeters?

a. rectangular prism (length = 10cm, width = 10cm, height = 3cm)
b. cube (side = 5cm)
c. cylinder (radius = 3cm, height = 10cm) - use π = 3.14
d. triangular prism (base = 4 cm, height of base = 3 cm, length = 10cm)

Explanation:

Step1: Calculate volume of rectangular prism

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

Step2: Calculate volume of cube

Volume formula for cube \(V = s^{3}\). Substitute \(s = 5\): \(V = 5^{3}=5\times5\times5 = 125\) \(cm^{3}\)

Step3: Calculate volume of cylinder

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

Step4: Calculate volume of triangular prism

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

Answer:

None of the options (a: \(300\) \(cm^{3}\), b: \(125\) \(cm^{3}\), c: \(282.6\) \(cm^{3}\), d: \(60\) \(cm^{3}\)) has a volume greater than \(300\) \(cm^{3}\). If we assume a typo and consider values close - none of the given options meet the strict "greater than \(300\)" criterion. But if we consider non - strict (greater than or equal, though the question says greater than), option a has \(V = 300\) \(cm^{3}\). If we re - check calculations:
For cylinder: \(V=\pi r^{2}h=3.14\times3^{2}\times10 = 282.6\lt300\)
For rectangular prism: \(V = 10\times10\times3=300\) (not greater than)
For cube: \(V = 125\lt300\)
For triangular prism: \(V = 60\lt300\)