29. A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 25 cm. (HINT: The altitude to the 25-cm side has length 12 cm.)

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Chapter65: Achievement Review—section Six
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Problem 55AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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418 CHAPTER 9 I SURFACES AND SOLIDS
29. A triangle has sides that measure 15 cm, 20 cm, and 25 cm.
Find the exact volume of the solid of revolution formed
when the triangle is revolved about the side of length 25 cm.
(HINT: The altitude to the 25-cm side has length 12 cm.)
30. Where r is the length of the radius of a sphere, the volume
of the sphere is given by V = r. Find the exact volume
of the sphere that was formed in Example 5(b).
31. If a right circular cone has a circular base with a diameter of
length 10 cm and a volume of 100 cm³, find its lateral
area.
32. A right circular cone has a slant
height of 12 ft and a lateral area
of 967 ft2. Find its volume.
"Hollow"
33. A solid is formed by cutting a
conical section away from a right
circular cylinder. If the radius
measures 6 in. and the altitude
measures 8 in.., what is the
volume of the resulting solid?
In Exercises 34 and 35, give a paragraph proof for each claim.
34. The total area T of a right circular cylinder whose altitude is
of length h and whose circular base has a radius of length r
is given by T
2 r(r + h).
Transcribed Image Text:418 CHAPTER 9 I SURFACES AND SOLIDS 29. A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 25 cm. (HINT: The altitude to the 25-cm side has length 12 cm.) 30. Where r is the length of the radius of a sphere, the volume of the sphere is given by V = r. Find the exact volume of the sphere that was formed in Example 5(b). 31. If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 100 cm³, find its lateral area. 32. A right circular cone has a slant height of 12 ft and a lateral area of 967 ft2. Find its volume. "Hollow" 33. A solid is formed by cutting a conical section away from a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in.., what is the volume of the resulting solid? In Exercises 34 and 35, give a paragraph proof for each claim. 34. The total area T of a right circular cylinder whose altitude is of length h and whose circular base has a radius of length r is given by T 2 r(r + h).
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