Add parser test.

multibody/parsing/test/detail_mujoco_parser_test.cc

@@ -823,6 +823,18 @@ TEST_F(MujocoParserTest, BadMeshSpatialInertiaFallback) {
   // that we're using it (and not choking).
 }
 
+// Ensure an exception is thrown for the mesh in bad_geometry_volume_zero.obj
+// since its calculated volume is zero (volume = 0).
+TEST_F(MujocoParserTest, BadMeshShouldThrowException) {
+  std::string filename = "drake/geometry/test/bad_geometry_volume_zero.obj";
+  std::string geometry_file_path = FindResourceOrThrow(filename);
+  const geometry::Mesh bad_geometry_volume_zero(geometry_file_path, 1.0);
+  DRAKE_EXPECT_THROWS_MESSAGE(
+      CalcSpatialInertia(bad_geometry_volume_zero, /* density = */ 1.0),
+      ".*volume of a triangle surface mesh is.* whereas a reasonable "
+      "positive value was expected. The mesh may have bad geometry.*");
+}
+
 TEST_F(MujocoParserTest, MeshFileRelativePathFromFile) {
   const std::string file = FindResourceOrThrow(
       "drake/multibody/parsing/test/box_package/mjcfs/box.xml");

multibody/tree/geometry_spatial_inertia.h

@@ -46,8 +46,8 @@ SpatialInertia<double> CalcSpatialInertia(const geometry::Shape& shape,
    - All triangles must be "wound" such that their normals point outward
      (according to the right-hand rule based on vertex winding).
 
- In the rare situation that we detect unmet requirements, an exception is thrown
- (no value is returned). Otherwise, the returned SpatialInertia is meaningless.
+ If `mesh` does not meet these requirements, then either an exception is thrown
+ (no value is returned) or the returned SpatialInertia may be meaningless.
  @throws std::exception if the volume of `mesh` is negative or nearly zero.
  @pydrake_mkdoc_identifier{mesh} */
 SpatialInertia<double> CalcSpatialInertia(