Solid Geometry: Chapter Test

Solution

Correct answer: C

You chose A: Chooses a parallel line that lies in the same side-face plane as AB.

You chose B: Chooses a line that meets AB at B.

You chose D: Chooses the opposite parallel line in the same base plane as AB.

Solution

Correct answer: A

You chose B: Multiplies the base area by the $11\text{ cm}$ joining edge instead of the perpendicular height.

You chose C: Adds the areas of both bases before multiplying by the perpendicular height.

You chose D: Treats the difference between the two lengths as the height and uses $23(11-7)$.

Solution

Correct answer: D

You chose A: Counts only three of the crossed faces, as though the plane necessarily clipped just one corner.

You chose B: Uses the number of sides of the prism base instead of the number of faces crossed.

You chose C: Adds the two base faces to the four crossings even though the four already count every face crossed.

Solution

Correct answer: B

You chose A: Multiplies by the first-to-second perimeter ratio, although the smaller perimeter needs the greater slant height.

You chose C: Uses the one-half area factor for only the first pyramid, doubling the needed slant height.

You chose D: Reports only the difference between the two slant heights.

Solution

Correct answer: B

You chose A: Cubes the diameter in the ball-volume formula instead of first halving it.

You chose C: Halves the volume after finding it, as if the given surface bounded only a hemisphere.

You chose D: Uses the sphere-area formula, $4\pi(19/2)^2$, for the enclosed volume.

Solution

Correct answer: D

You chose A: Uses the area factor itself as a length factor.

You chose B: Takes the square root of the first area divided by the second, reversing the requested direction.

You chose C: Treats the ratio of surface areas as a volume ratio and takes a cube root.

Solution

Correct answer: A

You chose B: Treats one move across a shared fold as enough to reach an opposite face. That fold leaves D and E sharing an edge.

You chose C: Tracks only the horizontal offset from D and misses the intervening change in row. B becomes opposite E.

You chose D: Assumes D and C face away from one another. Their shared fold is an edge of the cube.

Solution

Correct answer: C

You chose A: Adds the 9 cm slide to the perpendicular height, then adds the 3 cm rise.

You chose B: Keeps the height during the slide but subtracts 3 cm even though the apex moves away.

You chose D: Uses base area times height in both cases, omitting the pyramid factor of one third.

Solution

Correct answer: D

You chose A: Treats the full area loss as one copy of the patch.

You chose B: Finds the patch area and reports its number as a length.

You chose C: Divides the area loss by four as if four copies of the patch disappeared.

Solution

Correct answer: C

You chose A: Uses the perimeter of the generating half instead of the full axial section.

You chose B: Counts two slant edges but uses the radius as the full width.

You chose D: Rotates about the 10 cm leg, making the 24 cm leg the radius.

Solution

Correct answer: B

You chose A: Treats the off-axis width of $6\text{ cm}$ as the diameter, so uses radius $3\text{ cm}$.

You chose C: Swaps the axis and the off-axis width, using height $6\text{ cm}$ and radius $17\text{ cm}$.

You chose D: Uses the right radius and height but divides by three as for a cone.

Solution

Correct answer: A

You chose B: Uses the increase in volume, $343/216-1$, as the increase in area.

You chose C: Finds the length factor $7/6$ and subtracts one without squaring it.

You chose D: Uses the reverse area factor $36/49$ instead of the new-to-original factor.

Solution

Correct answer: C

You chose A: Adds the four pyramid triangles but leaves the covered square end in the prism's total.

You chose B: Adds only the pyramid's triangles, then subtracts the join twice from a prism total that contains it only once.

You chose D: Adds both solids' separate closed areas, leaving both copies of the joined square in the result.

Solution

Correct answer: D

You chose A: Drops the one-third factor and solves as though the cone were another cylinder.

You chose B: Uses the ratio of the radii, $6/9$, instead of the ratio of their squares to compare base areas.

You chose C: Triples the cylinder height to offset the one-third factor, treating the two bases as equal.

Solution

Correct answer: A

You chose B: Uses the disk radius of $12\text{ cm}$ as the ball radius.

You chose C: Uses the distance to the plane, $16\text{ cm}$, as the ball radius.

You chose D: Adds the disk radius and the distance to the plane to get $28\text{ cm}$, treating perpendicular legs as if they lay end to end.

Solution

Correct answer: B

You chose A: Counts the groove walls but leaves the two end rectangles that the groove removed.

You chose C: Subtracts the two end rectangles and accounts for the floor replacing the strip of top, but omits both new groove walls.

You chose D: Subtracts the top strip and two end rectangles and adds the groove walls, but omits the groove floor.

Solution

Correct answer: A

You chose B: Uses the $15\text{ cm}$ sector radius as the cone's perpendicular height instead of its slant height.

You chose C: Uses the correct perpendicular height and base area but omits the one-third factor.

You chose D: Treats $6\text{ cm}$ as the cone's diameter. With radius $3\text{ cm}$ the height would be $6\sqrt6\text{ cm}$.

Solution

Correct answer: C

You chose A: Sets both required tall columns in the back and leaves all front columns at height one, missing the required front row maximum of two.

You chose B: Adds the three front silhouette heights and the two right silhouette heights, counting the same tall column in more than one view.

You chose D: Fills all six sites to the overall maximum height of four, overriding the individual silhouette heights.

Solution

Correct answer: B

You chose A: Uses the material volume factor of $8$ directly as the length factor.

You chose C: Takes a square root of the material volume factor, as though it were an area factor.

You chose D: Finds the length factor of $2$ but applies it to the original outer radius.

Solution

Correct answer: D

You chose A: Treats radii drawn to the patch vertices as if they extended beyond the sphere.

You chose B: Confuses a plane through three distinct sphere points with a tangent plane.

You chose C: Treats all points of the face plane as points on the sphere instead of distinguishing the foot from the vertices.