Question

1. find the volume of the following figures.

a.
b.
c.
d.
(images of four figures: a pyramid, a pyramid with h=9cm and base sides l=4cm, a rectangular prism with dimensions 10, 4, 5, and a cone with radius 3cm and height 12cm)

Explanation:

Part a: Pyramid Volume

The formula for the volume of a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height. The base is a square with side \( 20m \), so \( B = 20\times20=400m^{2} \). The height \( h = 15m \).

$$ V=\frac{1}{3}\times400\times15 = 400\times5=2000m^{3} $$

Part b: Pyramid Volume

The base is a square with side \( 4cm \), so \( B = 4\times4 = 16cm^{2} \). The height \( h = 9cm \). Using the pyramid volume formula \( V=\frac{1}{3}Bh \):

$$ V=\frac{1}{3}\times16\times9=16\times3 = 48cm^{3} $$

Part c: Rectangular Prism Volume

The formula for the volume of a rectangular prism is \( V = l\times w\times h \). Here, \( l = 10 \), \( w = 4 \), \( h = 5 \).

$$ V=10\times4\times5=200 $$

Part d: Cone Volume

The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). The radius \( r = 3cm \), height \( h = 12cm \).

$$ V=\frac{1}{3}\times\pi\times3^{2}\times12=\pi\times3\times12 = 36\pi\approx113.04cm^{3} $$

Answer:

a. \( 2000m^{3} \)
b. \( 48cm^{3} \)
c. \( 200 \) (units not specified, assume consistent with given)
d. \( 36\pi cm^{3}\approx113.04cm^{3} \)