OML Sample Problems 2017 Meet 7 EVENT 2: Geometry Surface Areas & Volumes of Solids Include: Ratios and proportions Forms of Answers Note: Find exact answers (i.e. simplest pi and/or radical form) Sample Problems: A. Dilbert s fishpond is in the shape of a right regular hexagonal prism, top view shown below. The fishpond has a depth of 3 ft. Find the pond s volume. Answer: 81 3 2 ft 3 B. The radius of the base of a circular cone is 5 and the height is 6. Find the area of the cross section 2 units from the base. Answer: 100 π 9 C. Plane E intersects a right circular cylinder and is parallel to the line that contains the centers of the bases of the cylinder. Find the volume of the smaller spatial region of the cylinder that is cut off by E. Answer: 1280 π 320 3 units³ 3
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids April 2018 A. A right pyramid has height 3 and a square base of side 8. Find the total surface area of the (2 pts) pyramid. ANSWER: B. A sphere measures 4 inches around at its widest point. Four cuts are made that divide the (3 pts) sphere into 8 equal wedges. Find the volume of one wedge. ANSWER: cubic inches C. Buddy bakes a cake in the shape of a right circular cone with a diameter of 16 inches and a (5 pts) height of 15 inches. He makes a cut parallel to the base of the cone where the diameter is 4 inches. He eats the top of the cone and scoops out a cylindrical hole of diameter 4 inches all the way through the cake as shown. What is the volume of the remaining cake? ANSWER: cubic inches
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids April 2017 A. Region R is bounded by the positive x-axis, the positive y-axis, and the line 2x + 3y = 6. (2 pts) When R is revolved about the x-axis, a right circular cone is formed. What is the volume of this cone? ANSWER: B. A cylindrical container with a radius of 1.5 inches and a height of 10 inches contains 3 (3 pts) spherical balls each with a circumference of 8 inches. What is the volume of the space inside the container that is not taken up by the 3 balls? ANSWER: inches 3 C. A barrel in the shape of a right circular cylinder with radius 6 feet and height 8 feet (5 pts) contains water. When the barrel is lying so that its height is horizontal the depth of the water is 3 feet. What is the depth of the water when the barrel is turned upright so that its height is vertical? ANSWER: feet
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids April 2016 A. Joe just purchased his new cylindrical hydro flask. It is 16 inches tall and has a (2 pts) circumference of 5π inches. What is the volume of his flask? ANSWER: cubic inches B. A silo consists of a cylinder capped by a hemisphere as shown. The height of the cylinder (3 pts) is 20 meters and the diameter of the cylinder is 9 meters. Mr. Bailey wants to paint the exterior of the silo. What is the area of the surface that needs to be painted? ANSWER: square meters C. A cube is inscribed in a square pyramid as shown in the figure. The pyramid has slant (5 pts) height 10 feet and base length 10 feet. Find the surface area of the cube. ANSWER: square feet
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids April 2015 A. A sphere with radius 3 units has the same volume as a cylinder whose height is 1 unit. 2 (2 pts) What is the radius of the cylinder? ANSWER: units B. A sphere is inscribed in a right circular cone whose slant height and diameter are both (3 pts) 20 inches. Find the surface area of the inscribed sphere. ANSWER: square inches C. A regular triangular pyramid has volume 2 3 cubic inches. Each side of the base is (5 pts) 2 inches long. Find the length of the slant height. ANSWER: inches
Name Score School Event 2: GEOMETRY Surface Areas and volumes of Solids April 2014 A. A cylindrical cup is 5 inches tall and has a volume of 60π cubic inches. What is its radius? (2 pts) ANSWER: inches B. The diagonal of a cube is 15 cm long. What is the total surface area of the cube? (3 pts) ANSWER: sq cm C. A 150 sector of a circle with radius 12 cm is cut out of a piece of paper and then made (5 pts) into a conical party hat by taping together the radii of the sector. Find the volume of the hat. ANSWER: cu cm
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids April 2013 A. Find the total surface area of a square pyramid whose lateral faces are equilateral triangles. (2 pts) The side of each triangle is 12 inches. ANSWER: inches 2 B. A right circular cylinder has radius 6 inches and height 10 inches. A hole in the shape of a (3 pts) right circular cylinder with a 2 inch diameter is drilled from base to base. Find the total surface area of the cylinder with the hole. ANSWER: in 2 C. Given a sphere, a right circular cylinder, and a right circular cone. The sphere has the same (5 pts) radius as the cylinder. The cylinder has the same height as the cone, and the cone has the same volume as the sphere. If the surface area of the sphere is 144π, and the total surface area of the cylinder is 168π, find the total surface area of the cone. ANSWER:
Name Score School Event 2: GEOMETRY Surface Areas and Volumes of Solids A. Find the surface area of a sphere if its volume is 9π 2. (2 pts) ANSWER: B. A right circular cone with radius 8 3 feet has the top cut off, forming a frustum. The (3 pts) smaller right circular cone that was sliced off has a height of 9 feet and a radius of 3 3 feet. Find the lateral area of the frustum. ANSWER: sq ft C. A right prism has a regular octagonal base. All edges of the prism are 6 cm. A right circular (5 pts) cylinder of diameter 4 cm is drilled through the prism from base to base. Find the volume of the resulting solid. ANSWER: cm 3
Meet 7, Event 2: GEOMETRY Surface Areas & Volumes of Solids 2018 A. 144 B. 4 2 3π C. 270π 2017 A. 4π B. 45π 256 inches³ 2 2 π C. 8 2 3 feet 3 π 2016 A. 100π cubic inches B. 441π 2 square meters C. 12,600 7200 3 square feet 2015 A. 3 2 2 units B. 400π 3 square inches C. 327 3 inches 2014 A. 2 3 in B. 450 sq cm 25 C. π 119 cu cm 3 2013 A. 144 + 144 3 inches² B. 210π in² C. 108π + 12π 129 2012 A. 9π B. 330π C. 432 + 432 2 24π 2011 A. 864 in 2 B. 136 in 2 C. 288 2 cubic feet 2010 A. 144π m 2 B. 2 2 3 cu. ft. C. 108π 5 cu. units 2009 A. 9400π 3 cu. cm B. 2:3 C. 91π 4 2008 A. 32π 3 B. 300π C. 72 2 2007 A. 125% 3 B. 3 4 C. 12 + 4 3 2006 A. 294 sq. in. B. 50 + 15π sq. in. C. 261π cubic in. 2005 A. 672 cm 3 B. 40 π C. 6π 2004 A. 32π 3 B. 3600π square feet C. 5π square feet 2003 A. 104π 3 mm 3 B. 9 3 in 3 C. (48 + 8 3 + 6 π ) cm 2 2002 A. 726 square inches B. 160π 240 3 C. 184 2 3 2000 A. 40 3 π B. 174 2 C. 72 sq. meters Note: Answers are shown as they appear on the original answer keys. There may be inconsistencies with the formatting of these answers. In all cases, consult the Guidelines for Forms of Answers to determine the correct formatting.
1999 A. 3600 cu. in. B. 425π 4 3 2 C. A V 1998 A. 640 B. 16π 2 3 C. 300 + 150 2 1997 A. 30 B. 11,664π C. 90π 5 1996 A. 125 B. 24π 7 C. 864π 1995 A. 120 sq. in. B. 120 sq. units C. 37π 3 3 cu. units Note: Answers are shown as they appear on the original answer keys. There may be inconsistencies with the formatting of these answers. In all cases, consult the Guidelines for Forms of Answers to determine the correct formatting.