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andrezito [222]
3 years ago
12

Select the correct answer. What is the volume enclosed by the slanted prism in the diagram? A. 225 cm3 B. 270 cm3 C. 300 cm3 D.

540 cm3
Mathematics
1 answer:
artcher [175]3 years ago
5 0
A.225 cm3yiggjkkodjzkdjdjsjsgegwekwgwiwiehrirjlrotkrhrhr
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17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find
Pavlova-9 [17]

Answer:

r = 3.74cm

Step-by-step explanation:

Given

Hemisphere

Radius = 7cm

Cone

Height = 49m

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

V_1 = \frac{2}{3}\pi r^3

Substitute 7 for r

V_1 = \frac{2}{3}\pi * 7^3

V_1 = \frac{2}{3}\pi * 343

V_1 = \frac{686}{3}\pi

Volume (V2) of a cone is:

V_2 = \frac{1}{3}\pi r^2h

Because the lead is cast into a cone, then they have the same volume.

So, we have:

\frac{686}{3}\pi = \frac{1}{3}\pi r^2h

686 =  r^2h

Substitute 49 for h

686 =  r^2 * 49

Divide both sides by 49

r^2 = \frac{686}{49}

r^2 = 14

r = \sqrt{14

r = 3.74cm

<em>Hence, the radius of the cone is 3.74cm</em>

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Step-by-step explanation:

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