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8 votes
8 votes
Wey wey wonders how much water it would take to fill her cup. she drops her pencil in her cup and notices that it only fits diagonally. the pencil is 17 centimeters long and the cup is 15 centimeters tall. how much water can the cup hold? use paper to help you with your thinking.

User Singe Batteur
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1 Answer

16 votes
16 votes

Answer:

240π cm³ (exact)

754 cm³ (approximate)

Explanation:

I assume the shape of the cup is a cylinder. The height of the cylinder is 15 cm.

Think of a vertical rectangle that contains the vertical axes of the cylinder.

Two sides of the rectangle are diameters of the bases of the cylinder. The other two side are heights of the cylinder. The pencil is 17 cm long and is a diagonal of this rectangle. We can find the diameter of the base of the cylinder using the Pythagorean theorem.

In a rectangle that is 15 cm long, the diagonal measures 17 cm.

a² + b² = c²

15² + b² = 17²

b = 8

The diameter of the cup is 8 cm.

radius = 8 cm/2 = 4 cm

V = πr²h

V = π(4 cm)²(15 cm) = 240π cm³ (exact)

V = 754 cm³ (approximate)

User LeoQns
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