Geometry Answers

In the corner of a cellar is a pyramidal hoop of coal. The base of the hoop is an isosceles right triangle whose hypotenuse is 30ft. and its height is 8ft. What is the volume of the pyramidal hoop of coal in cu.ft.?

This figure is a rectangle with a semicircle on the shorter side. What is the perimeter of this figure? Use 3.14 for pi. 45.84 m 60.84 m 79.68 m 98.52 m

Tammy has a circular garden with a diameter of 36 feet. She will create 4 stone

pathways in the garden that will form an inscribed quadrilateral in her circular

garden. Tammy wants the straight-line distance between one pair of opposite

vertices to be 36 feet. She also wants two consecutive pathways to have

lengths of 24 feet and 12 feet. Tammy will plant marigolds along the shorter edge of

the garden that is cutoff by the pathways of lengths 24 feet and 12 feet.

What length, to the nearest tenth of a foot, of the edge of the garden will be planted

with marigolds?

A rectangle ABCD which measures 18 by 24 units is folded once, perpendicular to

diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

A piece of steel is in the form of a tetrahedron whose base is a right-angled triangle. The sides forming the right-angle are 5 cm and 6 cm long respectively. If the height of the tetrahedron is 7 cm, calculate its volume. If the tetrahedron is melted down, calculate the length of bar of diameter 20 mm that can be made from it, assuming no waste.

A circle is placed in a square with a side length of 12 cm, as shown below. Find the area of the shaded region. use the value 3.14 for r, and do not round your answer. Be sure to include the correct unit in your answer.

Can two or more three-dimensional solid figures have the same volume? Why or why not?

(08.02 MC)

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:

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Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? (4 points)

Group of answer choices

68.3

38.4

268.8

230.4

the radius of a cirlce is 5 kilometers. what is the angle measure of an arc bounding a sector with an area of 10 pie square kilometers?