Question

question 1
the height of a cylinder is 9.5 centimeters. the diameter of this cylinder is 1.5 centimeters longer than the height. which is closest to the volume of the cylinder?
a 1,150π cm³
b 287π cm³
c 165π cm³
d 105π cm³
b
a
d
c

Explanation:

Step1: Find the diameter of the cylinder

The height \( h = 9.5 \) cm. The diameter \( d \) is 1.5 cm longer than the height, so \( d=9.5 + 1.5=11 \) cm.

Step2: Find the radius of the cylinder

The radius \( r=\frac{d}{2}\), so \( r = \frac{11}{2}=5.5 \) cm.

Step3: Use the volume formula for a cylinder

The volume of a cylinder is \( V=\pi r^{2}h \). Substitute \( r = 5.5 \) cm and \( h = 9.5 \) cm into the formula:
\( V=\pi\times(5.5)^{2}\times9.5 \)
First, calculate \( (5.5)^{2}=30.25 \)
Then, \( 30.25\times9.5 = 287.375 \)
So \( V\approx287\pi \) \( \text{cm}^3 \) (since we factor out \( \pi \))

Answer:

B. \( 287\pi \text{ cm}^3 \)