Question

formula sheet (you may tear this page out.) general formula for volume or capacity of prisms and cylinders v = a_base h volume or capacity of a rectangular prism v = lwh volume or capacity of a cube v = s²h or v = s³ volume or capacity of a triangular prism v=(1/2 b_triangle × h_triangle)h volume or capacity of a cylinder v = πr²h 10. find the volume of the pentagonal prism with a base area of 25 cm² and height of 150 mm. 11. most candles are in the shape of a cylinder. to the nearest cubic inch, calculate the volume of a candle with a diameter of 3 inches and a height of 4 inches.

Explanation:

Step1: Convert units for question 10

First, convert 150 mm to cm. Since 1 cm = 10 mm, then 150 mm = 15 cm.

Step2: Apply prism - volume formula for question 10

The volume formula for a prism is $V = A_{base}h$. Given $A_{base}=25$ cm² and $h = 15$ cm, then $V=25\times15=375$ cm³.

Step3: Find radius for question 11

For a cylinder with diameter $d = 3$ inches, the radius $r=\frac{d}{2}=\frac{3}{2}=1.5$ inches.

Step4: Apply cylinder - volume formula for question 11

The volume formula for a cylinder is $V=\pi r^{2}h$. Substitute $r = 1.5$ inches and $h = 4$ inches. So $V=\pi\times(1.5)^{2}\times4=\pi\times2.25\times4 = 9\pi\approx9\times3.14 = 28.26\approx28$ in³ (rounded to the nearest cubic inch).

Answer:

1. 375 cm³
2. 28 in³