Question

a tomato sauce company currently sells tomato sauce in a cylindrical can that has a radius of 5 cm and a height of 15 cm. they have plans to use larger cans to sell tomato sauce in bulk. the new cylindrical cans are to be similar to the original cans and have a height of 60 cm. if the original can holds 79pi cm^3 of tomato sauce, how much tomato sauce will the new can hold?

Answer 1

The new cylindrical can with a height of 60 cm and a calculated radius of 10 cm will hold 6000π cm^3 of tomato sauce.

Step-by-step explanation:

The student wants to determine how much tomato sauce a larger cylindrical can will hold. Given that the original cylindrical can with a radius of 5 cm and a height of 15 cm holds 79pi cm3 of tomato sauce, and the new can has a height of 60 cm, we can calculate the new volume using the properties of similar solid figures.

Since the new can is similar to the original, the ratio of corresponding dimensions remains the same. Let's denote the new radius as r. We know from the original can that:

Volume ratio = (New volume)/(Original volume) = (New radius)2 / (Original radius)2

Hence,

(New height/Original height) = (New radius/5 cm)2

So we have:

(60 cm / 15 cm) = (r / 5 cm)2

4 = (r / 5 cm)2

r = 5 cm * sqrt(4)

r = 10 cm

The new radius is 10 cm. Now, we can calculate the new volume:

New volume = π * (10 cm)2 * 60 cm = 6000π cm3

Thus, the new cylindrical can will hold 6000π cm3 of tomato sauce.