- a.Since the triangular base of the vase is a right triangle with legs
of 4 and 6 inches, the area of this triangular base is A= ^12 (b)(h) =
(^12 )(4)(6) = 12 in^2. The vase is a foot and a half tall, which means it
is 18 inches tall. The total volume of water that the vase can hold is
V= 12 × 18 = 216 in^3. Since Miss Sweet is only going to fill it ^34
full, multiply the full volume of 216 in^3 by ^34 to get 162 in^3.
Set 72
- Volume= 546 cubic centimeters.The area of a seven-sided
figure equals one-half of its perimeter multiplied by its apothem:
perimeter of heptagonal base= 13 cm ×7 sides = 91 cm. Area of
heptagonal base= ^12 × 91 cm ×6 cm = 273 square cm. The volume of
a right prism is the area of the base multiplied by the prism’s
height: volume of prism= 273 square cm ×2 cm = 546 cubic cm. - Volume= 4.6 cubic feet.A pyramid with four congruent sides
means that this is a square based pyramid. Its volume is a third of a
cube’s volume with the same base measurements, or ^13 (area of its
base× height). Plug its measurements into the formula: ^13 (2.4 ft.)^2
×2.4 ft. Volume of square pyramid= ^13 (5.76 sq. ft.) ×2.4 ft. =
^13 (13.824 cubic ft.) = 4.608 cubic ft. - Volume= 1,100 cubic inches.Unlike the example above, this
pyramid has an octagonal base. However, it is still a third of a right
octagonal prism with the same base measurements, or ^13 (area of its
base× height). Conveniently, the area of the base has been given to
you: area of octagonal base= 330 square inches. Volume of octagonal
pyramid= ^13 (330 sq. in) ×10 in. = ^13 (3,300 cubic in.) = 1,100 cubic in.
501 Geometry Questions