Question

question 4 of 10
the two cones below are similar. what is the height of the larger cone?
a. \\(\frac{20}{7}\\)
b. 5
c. \\(\frac{28}{5}\\)
d. \\(\frac{35}{4}\\)

Explanation:

Step1: Set up similarity proportion

Since similar cones have proportional corresponding linear measurements, we set up the ratio of radii equal to the ratio of heights:
$\frac{\text{Radius of larger cone}}{\text{Radius of smaller cone}} = \frac{\text{Height of larger cone}}{\text{Height of smaller cone}}$
$\frac{7}{4} = \frac{x}{5}$

Step2: Solve for $x$

Cross-multiply to isolate $x$:
$x = \frac{7 \times 5}{4}$

Step3: Calculate the value

Compute the numerator first, then simplify:
$x = \frac{35}{4}$

Answer:

D. $\frac{35}{4}$